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Mathematician Explains Infinity in 5 Levels of Difficulty | WIRED
While the concept of infinity may seem mysterious, mathematicians have developed processes to reason the strange properties of infinity. Mathematician Emily Riehl has been challenged to explain infinity to 5 different people; a child, a teen, a college student, a grad student, and an expert. Director: Maya Dangerfield Producer: Wendi Jonassen Director of Photography: Ben…
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Jan Skoupý
January 30, 2023 at 11:39 pm
I don’t like logarithmic proof (not saying there aren’t more reals than integers, but it’s a feeling not proof). On one side of this proof are integers like 1,2,3,4… on the other side are reals as digits and for the creation a new number we change one digit of each number… So integers have infinite digits too (zeros before number – aka …0000001 as simple 1) and we can give integers on side of reals and integers will be uncountable… Other sight is on side of integers we choose not 1,2,3,4… but 1,10,100,1000… in this case we can create new reals but also integers too, and intuitively the same amount…
Logarithmic proof can’t prove identity, this is the same as in non-absolut convergent series, we can’t change order of elements, because we can change the sum of series.
Integers against reals have one weaknes… for integers exist base 1
Martin Christian Aguilar
January 30, 2023 at 11:41 pm
Möbius Strip
Eamon Reidy
January 30, 2023 at 11:42 pm
She’s one of the great category theorists
Abbaddonna
January 30, 2023 at 11:43 pm
Didn’t know Demi Moore was into maths 🙂
Soroush Rabiei
January 30, 2023 at 11:44 pm
That kid makes weirdly specific guesses (: Why 4012? Why not 4000? WHY? 😀
Adr
January 30, 2023 at 11:48 pm
commendable socratic method, very practical and comprehensible.
Boy Blue
January 30, 2023 at 11:50 pm
This makes my brain so hungry for math !!! This Masters enthusiasm about her Craft is Incredible !!!
notKamui
January 31, 2023 at 12:00 am
while she explains very well, she made a fatal mistake at some point.
It is very dangerous to admit Infinity as a number. You don’t do algebra with infinity, you only talk about limits. A side effect of allowing Infinity to be a number is to also admit that division by 0 is acceptable ; and at this point, you could prove, fallaciously, that 1 = 2
MuffinsAPlenty
January 31, 2023 at 12:35 am
There are plenty of contexts in which you can have a notion of number with infinite value. Cardinal numbers, ordinal numbers, hyperreal numbers, supernatural numbers, surreal numbers, etc. all have some notion of infinite-valued number. They’re valid concepts, but you have to understand that these types of numbers don’t necessarily behave the same way as other types of numbers you’re familiar with.
Zain Majumder
January 31, 2023 at 12:47 am
@MuffinsAPlenty The supernatural numbers are new to me! What a funny name.
Super PantMan
January 31, 2023 at 12:03 am
I watched this all the way through but didn’t understand anything after the high school girl
Rafał I
January 31, 2023 at 12:05 am
Concept of infinity is far to close to religion – in general it is just simplification of unknown. This video show it very clear, when child knows the topic pretty much as good as adults it is never a good sign. I hope someone will invent better/more useful concept for this problem.
Home Wall
January 31, 2023 at 12:10 am
These are explanations, but don’t make it any more clear in reality. That is, all positive integers will always seem smaller set than all integers because I can surely done a one-to-one mapping of all the positive integers in both sets, and will clearly have more unmapped on the 0 and negative integers.
Zain Majumder
January 31, 2023 at 12:40 am
First, a clarification: the mapping that we are looking for is called a “bijection”. First, the mapping needs to be one-to-one (each natural number gets mapped to its own element). Second, the mapping needs to be onto (no elements are unmapped to). So the example that you gave is one-to-one but not onto.
Two sets are defined to have the same cardinality if at least one bijection between them exists. I can demonstrate with two finite sets:
Set 1: {A, B, C, D}
Set 2: {E, F, G, H}
Obviously, the bijection {A -> E, B -> F, C -> G, D -> H} exists, so the sets have the same cardinality. But other mappings exist which are not bijections. For example, {A -> E, B -> E, C -> E, D -> E} is a valid mapping which meets neither of the qualifications for being a bijection. It doesn’t matter though, since we already found a bijection. We can just ignore the second mapping because we already know that set 1 and set 2 have the same cardinality. The same idea works for infinite sets. Since the video gave an example of a bijection, we know the set of positive integers and the set of all integers have the same cardinality, and mappings like the one that you gave do not change this fact.
iAMhonka
January 31, 2023 at 12:16 am
Somebody should explain her how a haircut works.
Shared Knowledge
January 31, 2023 at 12:18 am
I love how wired brings diverse smart appealing people to their videos. The presenter here is a perfect example. Please keep up these great videos!
Djamburere
January 31, 2023 at 12:22 am
Waw
King Snuffles
January 31, 2023 at 12:22 am
17:08 my new pickup line
juan martinez
January 31, 2023 at 12:26 am
I know some of these words
Guilherme Stahl
January 31, 2023 at 12:32 am
PLEASE WIRED NEVER STOP MAKING THIS SERIES.
(sory for yelling)
garret166
January 31, 2023 at 12:44 am
What I heard at @16:46 is that you could fill 3d Euclidean space with glitter no matter how thin or small the glitter so long as the glitter itself has a Real radius?
“That can’t have glitter in it…”
“You question MATHEMATICS ITSELF?!?!!?”
Ghostdog4
January 31, 2023 at 12:47 am
She is wonderful at getting the concept across. She could use a shoe shine.
Lucas Souza
January 31, 2023 at 12:49 am
“Ohh well..” Really loved that college student hahah made me nostalgic for my first semesters
8a40 dd88 4e5d
January 31, 2023 at 1:04 am
Excellent video!
Kyle Michael
January 31, 2023 at 1:06 am
i dont know, its pretty simple. infinite is infitine, so if theres an infinite # of sets then its the same as infinite, because its infinite.
gonda g
January 31, 2023 at 1:16 am
🤮
P A B
January 31, 2023 at 1:17 am
Connect to deeper than atoms what it’s made of ect the heaven state a flow shifting isness high awareness as well as periods of labelless connection moment becoming music itself becoming art mental landscapes new bodies and such. Intuition says this is a mode period solid fact yes the lower modes exist cause they just do it is the other side of that space does not mean abandon the lower as it does need improvement. All fearing aliens forest beings ect any comply strand focus w all you can intently to that false logic in that memory may be illusion other world yesterday info situation registers for who knows what will messes up unwill unwill messes up will not in the core. You truly connect to source mode can start screaming in joy and isness bawlling all egoic unnecessary conniving rough nonsense sheds world will return to compassion and into art more all immoral not w this will rot all night and asleep do not hurt yourself focus deeply on what that means
Anupam Kumar Gaurav
January 31, 2023 at 1:22 am
She is stupid.
Anxiety シ
January 31, 2023 at 7:44 pm
Next video
Zombie explains Zombie Apocalypse in 5 levels of difficulty
Sir Humble
January 31, 2023 at 8:08 pm
Ngl, The college student giving me Sheldon vibes
Danz English
January 31, 2023 at 8:32 pm
Next Applied Linguistics please, thank you
Ommi Sion
January 31, 2023 at 8:38 pm
Now do the same thing with a physicist 😀
Overload
January 31, 2023 at 8:38 pm
Seems completely intuitive to me that infinity + ‘whatever’ is simply infinity. That is what infinity is.
An interesting one to me is Infinity – Infinity. This seems to me to be a kind of inverted infinity, infinitely nothing, if you will.
I see it as the undefined on one side, and infinite possibility on the other, and definition somewhere in between, at a point to be defined, aka, relativity.
That is what N, Z, and Q, seems to be, they are this definition, they are quantization. A ‘let there be light’ if you will.
ValeryVal
January 31, 2023 at 8:56 pm
Children are way more intelligent than we get them credit for
Shilat's kalimba
January 31, 2023 at 9:03 pm
I mean, it doesn’t really belong here, but the college student is so pretty
David Landry
January 31, 2023 at 9:05 pm
I’m surprised that the nature of infinity wasn’t more thoroughly explained in terms of convergence vs. divergence, especially when talking about calculus and limits.
cameron
January 31, 2023 at 9:28 pm
only cardinal infinity, no ordinal infinity??
1.5x playback everything - thank me later
January 31, 2023 at 9:41 pm
Emily is amazing. wish we could get into her world of wonder
mark gray
January 31, 2023 at 9:42 pm
infinite just seems like mathematicians overthinking.
Dave Rodriguez
January 31, 2023 at 9:50 pm
The kid has such a solid grasp of infinity
Giovanni Frrri
January 31, 2023 at 9:50 pm
The biggest joke was when she said she teaches 🤣🤣🤣🤣🤣 university professors don’t teach lmao🥲🫠
hengis73
January 31, 2023 at 9:51 pm
Love the shoes!
Eug P
January 31, 2023 at 10:18 pm
Thanks Mr Riehl
James Fletcher
January 31, 2023 at 10:20 pm
love the maths videos, maybe a category with more real world applications would be interesting.
RG Astrofotografia
January 31, 2023 at 10:29 pm
Infinite sets don’t exist, as well as real numbers. Ask about this to @njwildberger and make a video in this channel @wired.
HKVC
January 31, 2023 at 11:35 pm
hmmm???
Ummer Farooq
January 31, 2023 at 11:40 pm
THOSE z integers look more like halving the weight of infinity.
Sufthegoat
February 1, 2023 at 12:10 am
Let’s goo
Eddie Entertainment
February 1, 2023 at 12:23 am
22:30 what a fascinating way to approach mathematics and possibly science in general
Da C
February 1, 2023 at 12:41 am
Here is easy way to explain. What is half between 0 and 1. Is 0.5. So what is half of that 0.25. So what is half of that diatance. There is infinite amount of numbers between 0 and 1
Silver Sleezy
February 1, 2023 at 1:04 am
Maybe this was what Gojo’s childhood education was like
Andrés Mora
February 1, 2023 at 1:04 am
My head exploded with Hilbert’s Hotel
Daniel Thron
February 1, 2023 at 1:21 am
I love when people have names that, if they were in a novel, would be too symbolically on the nose to believe. A mathematician with a name that is a homonym for ‘real’ discussing the unknowable nature of reality?’ C’mon, universe.
curlybrackets
February 1, 2023 at 8:38 pm
mathematician: “so how do you describe infinity”
kid: “infinite”
Bill Kong
February 1, 2023 at 8:45 pm
oh she actually gives the diagonalization proof
christr28
February 1, 2023 at 9:10 pm
0 ∉N
Bill Kong
February 1, 2023 at 9:10 pm
So we construct successive larger cardinalities by taking power sets but that seems like a clearly countable process right? You have a starting point of Aleph_0 and have a procedure for generating a set with cardinality Aleph_n+1 which you can take to a limit of Aleph_ ω or something which is unreachable (but maybe not actually a cardinal). What are these supposed unreachable infinite cardinalities and why does she think there are uncountably many?
Disastrum Damian
February 1, 2023 at 9:18 pm
Clearly, the choice to only use female professors and one that looks like a dude that fits in the LGBTQ was the sole purpose of this video
MuffinsAPlenty
February 2, 2023 at 1:10 am
Triggered much?
Indo
February 1, 2023 at 9:38 pm
Infinity has drove me nuts for years right when it starts to make sense it throws you another curveball
Zerkish
February 1, 2023 at 9:48 pm
Fascinating person to listen to 🙂
Ja-mez
February 1, 2023 at 9:49 pm
Is that a woman explaining science?
Womble ofWimbledon
February 1, 2023 at 9:50 pm
Infinities are fun. I presuppose the Deity as the fundamental level of reality, and a lot of infi ities are inherent in that proposition. For more, check out the Forward of the Urantia Book.
Luke
February 1, 2023 at 10:36 pm
Cardinal infinity alaph null
Hubajube
February 1, 2023 at 10:36 pm
Oop, I think they edited out something at the start of the Cantor uncountable continuum proof. I feel like there was a part about what that list meant first that got cut out.
Strikeslip
February 1, 2023 at 10:57 pm
she smart
Derrick Mwathi
February 1, 2023 at 10:58 pm
She was definitely flexing when she was communicating with the graduate
jhb
February 1, 2023 at 11:06 pm
i will never be as smart as these freaks/heroes. really amazing how they think
Queen Penguin56
February 1, 2023 at 11:22 pm
I studied a bit of set theory and infinite for an independent capstone project, especially relating to explaining the von Neumann hierarchy of sets, which hypothesizes and visualizes the set of all sets. This was like music to hear her talk about and explain infinites, and if I get into John’s Hopkin’s it would be really cool to meet her.
Chris Høydahl
February 1, 2023 at 11:25 pm
Such a blessing to have the second expert come on and give her take on the philosophical property of these games we play. The examples we use to explain infinity to young people and novices are so palpably absurd it drives me crazy.
I wish I understood the terms and concepts she used in her conversation with the PhD student, so I could get a sense of whether the nonsense continues into the more complex games that professional mathematicians play on infinity.
It seems to me, as an amateur clearly, as if we are constructing layer upon layer of math upon a concept of infinity that is too narrow to begin with. Or perhaps ill conceived. It seems trivial to me to point out the flaws in several of the simple games. Like the explanation for why the set of natural numbers and integers are the same size, or the conjecture that 1+1/2+1/4+1/8… =2. Even that 1+infinity somehow equals infinity.
It is “counterintuitive” because it is wrong… Yet of course, a broken clock is right twice a day, and these constructions clearly have practical applicability.
Hoganply
February 1, 2023 at 11:49 pm
Not being a math geek, let alone a methematician, my instinct was to conflate (or compare) a lot of infinity talk with conjuring a god-of-the-gaps of mathematics. I’m content to say that I’m not smart or knowedgeable enough, though, for this to be my belief.
Bendirval
February 2, 2023 at 12:05 am
Wow. I’ve seen a lot of these, but the discussion with the expert here was the most heavy duty, but also very fun. Two kids on a playground, all excited by a bunch of words I don’t understand in that context.
martı kanat
February 2, 2023 at 12:17 am
She looks like Gilbert Strang
Brandon Guffey
February 2, 2023 at 12:34 am
First saw Emily on Numberphile! Love hearing her explain things and see that she is continuing to do things!
Colin McIntyre
February 2, 2023 at 12:52 am
This was stupid and theoretical. I like the idea of this, but I disagree with a lot. It’s obviously more theory than fact. Infinite vs infinite isn’t the same as 0=0 and the fact they don’t get that or explain it well was depressing and made me upset also infinite is not always the same as infinite and if you don’t get that your not a expert on infinity. She seemed nervous the whole time, and like she was parroting her textbook and not thinking.
MuffinsAPlenty
February 2, 2023 at 1:27 am
It seems like you only understood up to the teenager level, which is totally fine! Professor Riehl’s use of infinity at that level was a “white lie” so to speak because she didn’t want to go into too many of the details of what specific type of infinity she was talking about on a level 2 explanation.
Solidfreeman
February 2, 2023 at 12:53 am
The only mysterious thing is the question how damaged your brain must be for that haircut and outfit. Go elsewhere.
Derin with a Q
February 2, 2023 at 12:54 am
People talk a lot about how some infinities are larger than others, but the infinity of the natural numbers always seems to be the smallest type. I’m curious, are there infinities smaller than the set of the natural numbers?
Brickzot
February 2, 2023 at 8:12 pm
“…I know you are but what am I?”
“You’re stoopid!”
“Oh yeah? Well _you’re_ stoopid *times infinity!* ”
And thus began, after that fateful day on the school playground at recess, the journey to search for the answer, the Last and Final Word, the ultimate comeback of all combacks that ever existed, an argument with an infinity bigger than any infinity out there, an infinity so great that it would transcend time and space and crush this argument to smithereens.
Teddy Tindle
February 2, 2023 at 8:14 pm
1:43 gimme a piece of jar rn
Don Bichoupan
February 2, 2023 at 8:30 pm
do bitcoin next!
Peezie Forestem
February 2, 2023 at 8:32 pm
CS student has been slacking off…
YawnGod
February 2, 2023 at 8:35 pm
The level of psy-op going on right now just staggers the mind.
I like this.
Mandy Caputo
February 2, 2023 at 8:44 pm
This kid sounds way more clever than I ever did and that was just the first level of difficulty 🤣
gabe guralski
February 2, 2023 at 9:29 pm
I’ve been waiting for this one. good vid
Dániel Faller
February 2, 2023 at 10:14 pm
That girl at the beginning is a genius. The idea that some infinities are bigger than others is mindblowing.
bec
February 2, 2023 at 10:18 pm
Not to be mean but I honestly mistook the 1st child, well the picture on the thumbnail, I thought that was Kylie Jenner before the surgery. I feel like an idiot
foo
February 2, 2023 at 10:29 pm
I watched 21:49 minutes of this video, she claims that infinity exists in this universe but cannot provide any examples. Wow.
J G
February 2, 2023 at 10:51 pm
And this is why atheists are small minded
Chris de Guia
February 2, 2023 at 11:08 pm
I followed as far as college student. Im guessing thats where my general knowledge ends. Therefore, in this exact moment, what I know, if it was quantified, is a finite amount. Yes.
꧁꧂
February 2, 2023 at 11:21 pm
I have an exam in set theory on monday and it’s crazy to think that I as a third year student can keep up with everything said in this video. Wild.
Loved it, can’t wait to hear more mathematics in this format ❤️
Nick Llama
February 2, 2023 at 11:23 pm
The kid is smart as heck. Sign her up for STEM!
Pablo JP
February 2, 2023 at 11:23 pm
The child was so smart wow
12many4you
February 2, 2023 at 11:34 pm
making that kid recite those responses is just weird and makes the expert look silly. hope they didn’t come up with that themselves
Pablo Vazquez
February 2, 2023 at 11:40 pm
20:42 lady in purple goes for the “listen here, im the expert and my time is finite”.
RedBlackDish
February 2, 2023 at 11:51 pm
Hilbert’s hotel flaw in logic: It doesn’t accomodate any more people because for every new person there is always one everchanging person in the middle of switching rooms.
Omar Acosta
February 2, 2023 at 11:54 pm
I liked skittles!
lucax tshotting
February 3, 2023 at 12:12 am
for someone taking a “calculus 2” course the computer engeneering student is a little underknowledged. Magnitudes of infinite are tied with limits and derivatives calculation, high school stuff.
Ugh really, im getting triggered thinking of it. I wouldve guessed anyone studying my degree knows there are infinte numbers of real numbers between two natural numbers.
Goes to show the issue with university: a university student doesn’t know what a 14 year old almost guessed.
maddsuaVFX
February 3, 2023 at 12:36 am
Mathematicians talking about the infinity, to me sound exactly like me to mathematicians, when I start talking about CPU registers
duskgleam
February 3, 2023 at 12:46 am
me watching as if I’m understanding anything
Hoony K.
February 3, 2023 at 12:50 am
I’d argue that it’s impossible for a person to count exactly how many glitter pieces are in that jar.
Randy Bugger
February 3, 2023 at 12:52 am
I’m glad someone enjoys mathematics. I guess I can be happy with enjoying their joy. Seems fair, right?
Graham Wellington
February 3, 2023 at 1:12 am
Fascinating concept.
This is the first one I had to stop at the high school level in order to research. I watched the rest but I couldn’t comprehend most terms or concepts below the high school level.
I’m a not a dummy, I’m an interested in learning dummy.
shar thor
February 3, 2023 at 8:25 pm
Is that a man or a woman
Penelope
February 3, 2023 at 8:37 pm
these comments are great
Gabriel de Santana Lacerda
February 3, 2023 at 8:46 pm
I want Emily to be my friend, she is so cool!
Blaze Miskulin
February 3, 2023 at 9:14 pm
You lost me half-way through “College Student”. When it comes to “infinity”, I’m rather happy with that. 😀
Steve Brule
February 3, 2023 at 9:27 pm
The language used to describe different sizes of infinity is insufficient to understand the concept. “More” or “bigger” are contradictory words to describe them.
The Creek Kid
February 3, 2023 at 9:40 pm
How does this mathematician look like a middle school boy and a middle-aged woman at the exact same time?
Dax
February 3, 2023 at 9:44 pm
I would love to do one of these!
Sergiu Sava
February 3, 2023 at 9:46 pm
She talks about infinity like it’s a great lover. Impressive eloquence!
Luke Sanford
February 3, 2023 at 10:01 pm
That is a wildly intelligent 9 year old.
Mark O'Connell
February 3, 2023 at 10:04 pm
Infinity has no center
Mughal
February 3, 2023 at 10:22 pm
imagine roger penrose as the expert in this
J Fizzo
February 3, 2023 at 10:26 pm
Watching the experts speak makes me realise how smooth my brain really is…
Sir MineCraft
February 3, 2023 at 10:46 pm
I wouldn’t even dare trying to explain it
Mateus Brum
February 3, 2023 at 10:51 pm
I’m a college student and the college student level already gets me confused
Zbyszek Jot
February 3, 2023 at 10:56 pm
I must say that was the most inclusive thing I’ve seen today.
Aiks
February 3, 2023 at 11:10 pm
i thought zero wasn’t a natural number
Santi04
February 4, 2023 at 12:39 am
yeah wtf
Orion
February 3, 2023 at 11:11 pm
A finite set divided by an infinite set equals infinity. Anything divided by Infinity equals infinity. There are greater and lesser infinities. A lesser infinity has an infinite amount of time to catch up to a greater infinity. But then, this needs a description of time.
So, well, this is just weird.
Cherd
February 3, 2023 at 11:36 pm
That youngest girl has a better grasp on infinity than 99% of adults.
Andreas Nolte
February 3, 2023 at 11:56 pm
One interesting aspect of what Elliot said about Projective Space, that parallel lines will intersect at point of infinity: I had a very big argument in my geometry class with my professor about that aspect, because I gave an presentation about that topic.
I argued, that it isnt a great description to say, parallel lines would intersect at infinity, because it disguises what happes really mathematically. So what happens?
You expand your normal space of points => You look at all lines in the geometric space and ADD their direction as an attribute as new points in the space: et voila, you get your projective space with additional points 🙂
Each line in the space now has an additional point, which is “lying” on that line: the direction of that line!
So when two parallel lines (ergo hey have the same direction) are intersecting each other, it means, they have a common point: their direction.
Projective space allows you to add attribute of geometric objects to the space itself, so you can let object like lines intersect in an shared attribute.
A real life example would be: in physics two seperate objects dont share any particle, like two humans. But if you now add attributes of a human per definition to the set of particles, you get new “physics”. Like person A and B have the same gender. Now they share a “physical particle”: their gender. 😀
I always found, that its more confusing to talk about “infinity” in this context.
BUT: I had my class many, many years ago and I am not sure, if I remember it correctly.
So I am open for correction in my argumentation 🙂 🙂 🙂
Emil Frei
February 3, 2023 at 11:56 pm
8:31
This question isn’t that easy.
If you’d asked a measure theorist, he would say there are both the same size.
If you’d asked a topologists, he would say no.
Because you find elements in { {Z }/ {N}} except of { } such as {-1}. So Z is larger than N for at least 1 element.
Same goes for open and closed sets.
Brack Zaff
February 4, 2023 at 12:07 am
Me: Heh, that college student hasn’t learned about cardinality of infinite sets yet. Also me: I wish I knew what the last two folks were talking about.
L3g3nd
February 4, 2023 at 12:19 am
do you have a favorite consequence of the axiom of choice?
Baneslayer™
February 4, 2023 at 12:21 am
I am so impressed by the kid at the start. She was awsome 🙂
ididn'tknowwhattoputhere
February 4, 2023 at 12:26 am
infinity makes me cry. just think about it.
even if you believe in reincarnation, there will be a last cohesive thought. mathematicians love studying infinity when applied to the world, but it simply does not exist. when applied to humans, there is no infinity. the universe is never infinite and every single creature that has ever existed will eventually die. the last cohesive thought will either be the realization of fate or the will to survive, and once we all realize that there is no infinite, we can accept the fact that humanity will never exist compared to infinity. there is no infinity amount of time. there is no infinite human.
There is no infinity.
aaaaa
February 4, 2023 at 12:48 am
They shouldve brought in dr z
mucxlx
February 4, 2023 at 8:42 pm
The only thing that can be infinite is nothing
jpatkins34
February 4, 2023 at 8:55 pm
This was very cool. If someone hasn’t said it yet, Professor Riehl needs a podcast or show or something called “All Riehl Numbers.” Then she can end each show by saying “this has been Emily Riehl for All Riehl Numbers.”
Jonny Turtleneck
February 4, 2023 at 9:16 pm
Just tell the kids about the infinity stones
Kyle Blaszyk
February 4, 2023 at 9:29 pm
When talking about sizes of infinity is it possible that infinity exists in something finite? For example, are there an infinite amount of numbers between 1 and 2?
1thomson
February 4, 2023 at 11:10 pm
Yes.
Cesare Piemontese
February 4, 2023 at 9:32 pm
“Mathematicians think of infinity as a number”. My analysis prof at the first lecture of the semester: “ok guys let me be very clear, infinity is NOT a number, stick this into your mind”
SinkerSnaps LLC
February 4, 2023 at 9:32 pm
Have mathematicians been able to connect the math defining infinitiies with probability of things happening or not happening in a finite sense? For example, what is the probability of that monkey typing Hamlet?
Omar Galvez
February 4, 2023 at 9:51 pm
I have just consumed the devils lettuce and i am ready for this video
Omar Galvez
February 4, 2023 at 10:05 pm
I dont know man
Punisher
February 4, 2023 at 10:11 pm
She was more interested in talking with the grad student than any of the others.
MannaMansikka
February 4, 2023 at 10:20 pm
The way I’m in seventh grade (1st grade of swiss long gymnasium) and the same stuff she talked with the college student about, I already had earlier this year.
Low Eel
February 4, 2023 at 10:24 pm
She should have used Aleph Zero. Infinity is NOT an amount, NOT a number, neither is equal to any number. Aleph Zero is a transfinite cardinality, not infinity.
denoiser
February 4, 2023 at 10:35 pm
Sorry in advance, i don’t want to troll your chanell, but curiosity killed the cat and without any mockery…. Is this presenter man or woman?
krollic
February 4, 2023 at 10:50 pm
it is a troon
MuffinsAPlenty
February 4, 2023 at 11:24 pm
Emily Riehl is a woman.
krollic
February 4, 2023 at 11:28 pm
@MuffinsAPlenty non-sense. the physiology does not lie
Phoenix
February 4, 2023 at 10:35 pm
yo why her eyes purp fr?
Tanmay Rajendra Bhore 17302
February 4, 2023 at 10:49 pm
Brilliant video, brilliant host. Her enthusiasm is infectious!
krollic
February 4, 2023 at 10:53 pm
there is an infinitesimally small probability that that is a woman
igor ostrovski
February 5, 2023 at 12:56 am
Lmao i was searching for a comment that said that. Looks like a trans
alternatereality8
February 4, 2023 at 10:56 pm
LOL that grad student whipped out Banach Tarski and she was way out of her depth
MuffinsAPlenty
February 4, 2023 at 11:18 pm
Your username is apt because you must live in an alternate reality to come to that conclusion after watching the video.
Britannia Freya Day
February 4, 2023 at 11:26 pm
This was infinitely and painfully un educational & un enlightened, the very epitome of why you should not put your kids into so called “higher education”
Every single person that watches this will come away less intelligent and more confused about the reality they live in,
truly a disservice to the people.
The most intelligent individual in this was the child in the beginning,
may god help her preserve her natural spark if she goes into the indoctrination camp.
Gregory Zak
February 4, 2023 at 11:40 pm
But can the ideas go countably on and on forever?
Ok I’ll show myself out..
Melissa Holibaugh
February 4, 2023 at 11:43 pm
Wish she was my teacher in High School. I might have been excited by math. Lol
yt addict
February 4, 2023 at 11:48 pm
What color is your Bugatti ?
shune84
February 4, 2023 at 11:52 pm
“i would say about 217” that was a pretty specific number
Reindert D.
February 5, 2023 at 12:00 am
Infinity = infinity. I find it a simple to understand concept.
Trying to prove it through math however can be very complex it seems, which I do not find simple at all xD.
Ollecram 8867
February 5, 2023 at 12:15 am
Size and infinity doesnt match 2:32 . I think infinity is and will always be soemthing people cant figure out no matter what. F.e. Think about there was a time before us and it existet infinitely. We‘d always try to think back and back in time but infinity is infinity
Russell
February 5, 2023 at 12:35 am
I love her.
brandon castro
February 5, 2023 at 12:54 am
math is a sense as thought is empty
Paul Simon Rough
February 5, 2023 at 12:58 am
What I’m learning here is that most documentaries on TV are in child level.
Gold, Jerry! Gold!
February 5, 2023 at 9:22 pm
Poor computer science guy is so awkward. As a fellow awkward computer science guy I feel him
Steven Rogers
February 5, 2023 at 9:31 pm
00:11 “It’s very difficult to find infinity in the real world”. . . . . Have you ever heard of the Law of Conservation of Mass? Lol
If something cannot be created, or destroyed, it is infinite. Therefore, literally EVERYTHING around you is infinite lol.
Zack Lambert
February 5, 2023 at 9:42 pm
I have a problem with hilberts hotel, it shows the rooms starting with 1 and then turning into infinity. Wouldn’t a infinite hotel be infinite in both directions?
Tomas
February 5, 2023 at 10:03 pm
Infinite only means that the set of rooms is not finite. Since the set of natural numbers is not finite (for every finite number you can show there are more natural numbers), it is infinite
Zack Lambert
February 5, 2023 at 10:10 pm
@Tomas so infinity can have a starting point?
Boštjan Gabrovšek
February 5, 2023 at 10:02 pm
The talk with the phd student was more difficult and technical than with the expert
Shersingh Saini
February 5, 2023 at 10:15 pm
She is so real for that!
WallE
February 5, 2023 at 10:20 pm
What a smart child. Much smarter than me 😂
Jean-Baptiste
February 5, 2023 at 10:25 pm
Me trying to check the vidéeo speed
Bognár Péter
February 5, 2023 at 10:26 pm
lost me at Phd lvl
Varen Wilson
February 5, 2023 at 10:42 pm
She would be the best math teacher
minmb82
February 5, 2023 at 10:57 pm
how many genders are there? Infinity no?
Ramon Garrison
February 5, 2023 at 11:02 pm
This is just like the vsauce video
1.5x playback everything - thank me later
February 5, 2023 at 11:03 pm
keep coming back to this vid. I think one time someone said “if you don’t understand something, come back later 5 years, they will figure out how to explain it to high school students”
Víctor Matheus
February 5, 2023 at 11:11 pm
This is easy, I wanna see you explain 5 in infinity levels of difficulty
Matthew Lawson
February 5, 2023 at 11:11 pm
Ok that young girl is way more intelligent than most her age. That’s impressive.
Active Advocate
February 5, 2023 at 11:19 pm
You lost my math brain talking to he teenager: I didn’t do much in the way of high school math. BUT, you got me back on again when talking to the expert about the philosophy of math, because I was a philosophy student in university. There could potentially be infinite infinities, because, for example, 1, 2, 3, 4, that goes on forever. But ALSO, 1, 1.1, 1.01, 1.001, just keep adding zeros, THAT goes on forever, but ALSO, 1, 1.1, 1.10, 1.100, keep adding zeros on the other end, THAT goes on forever, but again, 1.1, 1.2, 1.3, 1.4, just keep adding numbers, and you can keep doing all of those patterns forever. I don’t know if it’s so much about how many kinds of infinity there are so much as it’s about how and whether they function, because you’ll start to get ino the realm in which numbers no longer have utility. There’s also spatial infinity–see Zeno’s Paradox. But with ANY kind of infinity, it’s infinite because you could always add another division on either end of the thing. But THAT, still, is only infinite WITHIN itself. What about outside of itself? Well, now you’ve really thrown the doors open. I, for example, the Universe is infinite, and, to my knowledge, while unimaginably large, since it’s EXPANDING, then no, it’s not infinite, but then, what is it expanding into? I don’t mean “What form will it take?” I mean, “What’s the thing outside of the Universe into which it is expanding itself?” Space outside space, in other words. But that’s now into astrophysics, and if you think THIS is idiotic, you should see me around physics. I like it, though: I like feeling stupid in this regard, because it means that my brain-Universe still has space to grow out into.
Blanche Greco
February 5, 2023 at 11:27 pm
I’ve now figured what I want to do in life now: become a mathematician
ket.
February 5, 2023 at 11:33 pm
Bro I have no clue what they were talking about later on
Matthew W
February 5, 2023 at 11:46 pm
Why’s she got a man’s haircut?
Anthony Faiell
February 5, 2023 at 11:57 pm
Ah, talking about inifinity, something that holds absolutely 0 relative value to anything practical whatsoever.
cracqheadish
February 6, 2023 at 12:14 am
Off topic but that 13-year-old looks a lot more mature than I’d imagine a 13-year-old to look like. at my school they’re usually in the 4 foot range or low 5 foot
Marwan Elbattouty
February 6, 2023 at 1:02 am
Bruh the first child just figured it out and the mathematician went on and on, USELESS
Tom Watson
February 6, 2023 at 1:02 am
It wasn’t to long before I waded out deep enough that I was drowning, for her it must be the same looking in to the singularity of infinity
MilkyClick
February 6, 2023 at 1:18 am
I’m happy that at my age of 14, I understand the level of a college computer science student, because of me liking Vsauce’s content.
Elijah Cisco
February 6, 2023 at 1:20 am
did Emily calculate mimicing each of their body languages too?
Llaura M
February 6, 2023 at 1:23 am
brilliant video!!
sharkboy
March 2, 2023 at 11:59 pm
Youngest girl has alot of potential in the future
Marshall Cierovola
March 3, 2023 at 12:48 am
I don’t get the pont of the hotel scenario. Why move every resident to a new room instead of just adding the new resident to a new room? There isn’t a “last room” there isn’t a “last resident” they are both infinite. If you can add to it, it wasn’t infinite.
Alex Vickers
March 3, 2023 at 6:59 am
Since before time and space were,
the Tao is.
It is beyond is and is not.
How do I know this is true?
I look inside myself and see.
jean jacques jell
March 3, 2023 at 8:48 am
GOSH SHE’S SO SMART AND MAKING THIS ABSURD SOUNDING CONCEPT SOUNDS SOMEHOW UNDERSTANDABLE although I’m already using a week worth of brain energy lol…
Prayag Sharma
March 3, 2023 at 9:09 am
That child really has the potential to really well in the field of science.
Mark Smith
March 3, 2023 at 10:49 am
Infinity means all- infinite glitter means you can’t anything else so so no bottles. An infinite hotel has no people that would place a limit on it- it has no limit. Once you have infinite integers, integers cease to make sense henceforth there are the same number of integer as real numbers because the integers become real numbers. . Mathematican fails on logic.
Tomas
March 4, 2023 at 8:34 am
Nope, that’s not what infinite means and everything you said was wrong
Mark Smith
March 4, 2023 at 8:47 am
@Tomas Yes it does mean that- no means no limit.
Mark Smith
March 4, 2023 at 8:58 am
@Tomas The number mathematicians really mean is Large- an indefinitely big number that is big enough to do what ever you want it to which always smaller than infinity.
Tomas
March 4, 2023 at 9:21 am
@Mark Smith we’re not talking about infinite as a number. It’s a property of a set. And a set is infinite if it’s not finite. Both the set of natural numbers and the set of real numbers are infinite, but you can’t pair them up. There are simply too many real numbers
Alexis Fung
March 3, 2023 at 4:13 pm
Idk why but my first thought, when she asked “do you believe in the axiom of choice”, was that it was the most culty non-cult thing I have heard lol
Errol Fouquet
March 3, 2023 at 6:49 pm
It’s turtles all the way down.
Chonalyn PAK
March 3, 2023 at 7:31 pm
Infinities have different sizes
V Volka
March 4, 2023 at 5:36 am
AH ! the usual expert lvl 5, where my brain automatically shuts downs .
sound_file = infrasonic waves 💣
Evan B
March 4, 2023 at 9:45 am
We question the abstract and infinity because we are made in the image of God.
Joshua Hemming
March 4, 2023 at 11:22 am
Infinity sits between 0 and 1.
Neil Walker
March 4, 2023 at 7:50 pm
Amazing and simply insightful
Caleb Quittner
March 5, 2023 at 3:48 am
Wouldn’t a great application of infinity be in quantifying the apathy that most humans have towards eating torture animals? Blah blah blah blah blah (ad infinitum)
tapioco71
March 5, 2023 at 8:40 am
La figlia di Luca Sardella?
kiwigirljacks
March 5, 2023 at 9:11 am
My brain just exploded.
biggie smith
March 5, 2023 at 11:34 am
unlimited pieces of jar💀
Mary Juana
March 5, 2023 at 12:13 pm
…and beyond?
Rich Life
March 5, 2023 at 12:18 pm
Hilbert’s Hotel is inherently flawed because there is an assumption that there is a starting point. Infinity, by definition, can’t have a starting point. If you were to start at hotel room #1, you would also need to have hotel room #-1 directly adjacent to it and counting backwards into infinity as well, meaning you cannot vacate starting with just the one room. You are essentially creating a flawed theory in this example. We do the same with numbers, thinking that the #1 is our starting point for counting. But wherever there is a 1, there is a -1, and so on and so forth for every number that you could possibly conceptualize.
kumkum's lab
March 5, 2023 at 1:27 pm
what do you want to explain…………………….
kumkum's lab
March 5, 2023 at 1:27 pm
infinity is like while(True){
goes ON…..
}
ralf fig
March 5, 2023 at 3:09 pm
The expert is a master bullshitter.
Dennis Kane
March 5, 2023 at 6:07 pm
I don’t think that a function is necessarily isomorphic or one-to-one, right? A function can be many-to-one, just not one-to-many.
frottery
March 5, 2023 at 10:15 pm
When you mention “intutition” you are talking about where people with zero advanced mathematical understanding begin. To state that infinity is the same size for integers and natural numbers requires the ignoring of “time” per calculation. ie, at any given interval you will always have less of the integer set calculated than the natural number set.
I’m stuck at the idea that if you calculate every second in parallel on two identical machines, after 1,000,000 seconds you have 0->999,999 natural numbers as well as integers, but we know that integers would also include -999,999->0, so that same caluculation is less complete of a definition of the full set.
This just appears as a parlour trick since you can handwave away the line or set with “well, …infinity” on both to magically make up the time needed for those to be equivalent, when integers would effectively require double the calculation time to have the same fraction of the set represented. The grammar school trick of saying “infinity + 1 > infinity” is that intuition that wherever machine_1 is at calculating a set towards infinity, some other machine could be 1 step ahead.
And so, intuitively it is absurd to assert the infinity referring to the number of integers is “the same” as the infinity of the number of real numbers when one of those sets necessarily has more datapoints within them. It seems like a category error to me, where infinity is representative of “everything” or “endless process” which ignores what the product of that process is at any point along the currently calculated set.
If you replace infinity with “if you count forever”, or perhaps more accurately “you could count forever and never reach a conclusion” that is adding a new variable of time to the mix, and two machines in parallel cannot have counted the same fraction of those sets. And so it is no surprise that the light at the end of the tunnel is “philosophical” (placeholder to mean non-quantified) and out of the realm of quantification/logic. So the end folds on itself where the discussion about “sizes of infinity” because any attempt to practically calculate it is met with a limit to how complete those sets could be at any interval. There are an infinite number of real numbers between 0 and 1, there are an infinite number of integers, there are an infinite number of natural numbers. Yes, those are all equal but due to this category error of process and product I’m not grasping how they could ever contain the “same accuracy” regarding set definition.
Zero Music Talent
March 6, 2023 at 1:59 am
Pretty smart gal.
M
March 18, 2023 at 2:28 pm
double it and give it to the next person
Sami
March 19, 2023 at 11:26 pm
Why kids always have the best answers?
“It makes me feel like my brain is exploting” 😆
Serenity Skies
March 20, 2023 at 1:27 pm
The Hilberts hotel reminds me of an infinite pyramid scheme.
Emily Stepan-Jackson
March 20, 2023 at 1:58 pm
i loved seeing how she interacted with all the different people. never talked down to anyone and she really explained everything quite well.
Ethan Hayden
March 20, 2023 at 3:43 pm
I got lost at the teenager part lol
Shemiah Walker
March 20, 2023 at 5:31 pm
I like this topic
Insanity
March 20, 2023 at 6:09 pm
if we apply the 3x+1 conjecture to infinity it will give us infinity, no matter how much we divide or multiply it, right? (I believe that the 3x+1 conjecture does not apply to infinity, since we do not know if it is even or odd, but in both ways it would be infinite, because being multiplied or divided it will remain infinite)
Tomas
March 21, 2023 at 3:28 pm
We actually know if it’s even or odd. It’s neither. The property of being even or odd is only defined for integers and ‘infinity’ (whatever you might mean with it) is not an integer
Logan
March 20, 2023 at 10:24 pm
Duuude the kid is actually so smart
Kai Perdaens
March 21, 2023 at 2:24 am
U should watch the video that Veratisum made about an infinite hotel that runs out of rooms(Wilburt hotel)
Aayush Nirupam
March 21, 2023 at 4:18 am
she looks like anna hathaway
Classic Science Fiction & Horror
March 21, 2023 at 6:53 pm
Christian apologist and infinity-denier William Lane Craig checked into Hilbert’s and he can’t check out.
Owen M
March 21, 2023 at 10:40 pm
The first girl is smart asf
Ryan Buchanan
March 21, 2023 at 11:42 pm
Riehl is so cool ❤ man I loved Category Theory in Context
Sayan Das
March 22, 2023 at 1:54 am
The youngest girl is the most smartest one, I think
Vincent Karanja
March 22, 2023 at 8:25 am
Level 2: Sade
capitalist society bots
March 22, 2023 at 10:33 am
so basically, in the end, its just the anthropology of how humans grasp infinity
pavan kumar
March 22, 2023 at 11:00 am
She said natural numbers and has show 0 on the line 😂😂😂😂😂😂
Tomas
March 23, 2023 at 2:33 pm
Because in set theory (and many other areas in mathematics) we almost always include 0 in the natural numbers
Drax
March 22, 2023 at 2:38 pm
Yoni looks like someone would die first in a horror movie 😂 While Elliott feels like that mad scientist villain
Harry Pereye
March 22, 2023 at 11:19 pm
They lost me on the College level 😅
Hitsujikai
March 23, 2023 at 12:39 am
This kind of stuff fuels my brain. Call me a nerd or whatever
yog seventy-nine
March 23, 2023 at 12:22 pm
i stopped understanding after the first kid, i’ll pretend it’s only because english is not my mother tongue…
Sen Pie
March 23, 2023 at 2:27 pm
she is the math final boss
HisRoyalJazness
March 23, 2023 at 5:39 pm
That is a gifted child!
YuuKisane
March 23, 2023 at 5:40 pm
All the math black magic blasphemy aside, Emilys hair is stunning imo. Pretty simple, but fits her so well
Spajdi
March 23, 2023 at 7:33 pm
Me being happy i totally understood the conversation between her and a grad student. Than i remembered i am also a grad student…
EowynG191
March 24, 2023 at 4:12 am
So impressed with that child! I loved every single person chosen and the conversations they had!
Valentina Paxley
March 24, 2023 at 4:55 am
The level 1 girl had a very clear picture of infinity in her mind
مهندس برمجة
March 24, 2023 at 5:41 am
About “Hamlet and the typewriter” one simple answer existing of infinity doesn’t mean existing of what you wish “Hamlet”
In π there is no “9999999999999”
Emilia Wrede
March 24, 2023 at 7:31 am
i love seeing so many really smart girls and women here <3
mohan palaniyappan
March 24, 2023 at 10:39 am
Grace Wiredu
March 24, 2023 at 11:59 am
moin khandaker
March 24, 2023 at 1:05 pm
I am astonished at her extraordinary expertise😮
Allan Matano
March 24, 2023 at 4:44 pm
To me the college student and grad student display a more in-depth grasp of the subject matter than the expert.
Catana
March 24, 2023 at 5:11 pm
W Jew
Fish
March 25, 2023 at 6:55 am
Something I thought was really interesting was how it was almost easier to understand the two experts talking then the grad student. The way that the experts were able to explain their very thoughts was incredible.
Banana Monster
March 25, 2023 at 8:38 am
me who thinks infinity into infinity is absolute.
the bully of the school : i’m gonna put some 1 in your eye
me: huh?
TOP 10 MOST
March 25, 2023 at 8:57 am
she said “as a number infinity is very strange” hehe Women!!
Infinity is not a number its a symbol a constant it never increases nor decreases
Gabby Wolfgang
March 28, 2023 at 3:18 pm
Infinity isn’t a symbol or a constant, it’s a concept. Nice try though
Lai Lai
March 25, 2023 at 5:40 pm
The diagonal argument is nonsensical. Wish people admitted that
ExtravagantPanda
March 25, 2023 at 8:13 pm
Except it isn’t, there’s nothing to “admit”. It can be very unintuitive, sure, but it isn’t nonsensical, it’s precisely the opposite.
Genio Matematico
March 25, 2023 at 6:29 pm
cos’è l’infinito?
Voglio una traduzione di tutto il video in italiano qui nei commenti
Value
March 25, 2023 at 8:24 pm
Yes imagine infinitely many jars..the kid actually expose your stupidity self claimed priests of infinity religion.Clowns
Rebecca Butler
March 26, 2023 at 12:20 am
shouldn’t it be technically possible to fit infinite amounts of the jars in the room as the space could hold them until they compressed and produced enough energy to be a black hole, and then continue absorbing the jars forever?
skadoodle
March 26, 2023 at 9:44 am
Its ms. White and she sells MATH!!!!
danial jeelani
March 27, 2023 at 2:46 am
Hmm never thought Ellen DeGeneres, Was a mathematician
Ae Ea
March 27, 2023 at 10:40 am
I already failed at level 3
Murad Alrousan
March 27, 2023 at 11:10 am
Is she or he man or women i cant tell
Gabby Wolfgang
March 28, 2023 at 3:17 pm
…woman
Someone having short hair confuses you that much?
David Troyer
March 27, 2023 at 12:42 pm
I wish Emily was my discrete math professor
Raphael
March 27, 2023 at 3:42 pm
just say it never ends.
Coco
March 27, 2023 at 11:27 pm
I miss the times when these videos were not 100% scripted
Jeroen Kuijpers
March 28, 2023 at 4:34 am
I lost her completely after level two..
reinhard tristan eugen
March 28, 2023 at 8:36 am
Ein gutes Beispiel ( …und gleichzeitig eines meiner Lieblingsthemen, wie alle gleich wieder sehen werden, die meine Kurznoten kennen… ) für Unendlichkeit in der realen Welt, enthoben aller Abstraktizität sozusagen, ist die Quantenphysik mit ihren Wellenfunktionen🙂🙃😊, denn der Vektorraum der Wellenfunktionen ist unendlichdimensional. Das bedingt, dass es für die Quantenphysik Zusatzforderungen geben muss, um sich ihrer mathematisch nähern zu können, denn aus mathematischer Sicht sind die Zustände der Quantenphysik Grenzwerte und die müssen physikalisch sinnvoll sein, sie dürfen also nicht außerhalb des Vektorraumes liegen, und daher reichen die Forderungen für endlichdimensional ( Vektorraum mit Skalarprodukt ) auch nicht aus. Der Vektorraum muss zusätzlich vollständig sein, was heißt, dass rationalen Zahlen erweitert werden müssen durch die irrationalen Zahlen, sodass die Zustände, die man bekommt, sich innerhalb des Vektorraum befinden und über die Cauchy-Konvergenz kann man sich dem gut nähern finde ich. Darüber hinaus muss der Vektorraum separabel sein, was – hier nur vereinfacht – ausgerückt meint, dass es ein unendlich ist, das aber noch handlebar ist. Dazu ist es notwendig, dass die Eigenwertzustände eine Basis des Vektorraum sind, was bedeutet, dass alle möglichen Zustände darstellbar seien als Linearkombinationen.
Unendlich war auch eben die Woge meiner Maternalinklination, als ich die mir unbekannte Zuckerschnute erblickte, die da den Kontrapunkt zu Ben Shapiro bildete… …natürlich überlegen in Semantik und Rhetorik und Ätiologie… …weshalb ich hier noch mal meinen Adoptionsvakanz indizieren möchte, damit das hier nach dieser unerträglichen Unendlichkeit bald endet…
Le p’tit Daniel
Putin’s Gay Twin
March 28, 2023 at 11:38 am
How the heck can infinity get bigger?
Dana Shafir
March 28, 2023 at 1:32 pm
This is wonderful
Andrew
March 28, 2023 at 4:08 pm
lmfaooooo 3:03 her reaction 😂😂😂 “really…. wow…. ok…..” she’s so uninterested
jaassil
March 28, 2023 at 7:12 pm
Next level you need to talk to God himself.
suman
March 29, 2023 at 6:40 am
This is confusing to me if the universe is expanding that means it can get bigger if it can get bigger it hasn’t reached it complete capacity yet for infinity to exist it needs infinite space space is expanding forever even forever is not infinite eventually in the far future even space itself will die out because of entropy entropy too will die out after the universe can’t get any more distorted .so space can’t have infinity .infinity is just a concept that doesn’t exist didn’t exist and will never exist in the universe.stars also looks infinite to the human eye because u can’t see everything stars are not infinite they rapidly increase if something can increase it means it has more space to expand into which also mean it has a limit if space itself is expanding and will stop things inside it can’t be infinite or forever cells dust atoms particles radiation light nothing is infinite it’s just a concept that doesn’t exist.it only “exists” mathematically even when your “showing” infinity as a number it can’t be shown because it doesn’t exist the only way u can kind of “show” infinity is with a line above the number that’s “infinite”
Mina Kadri
March 29, 2023 at 10:47 am
the kid is incredibly smart
The Joker
March 29, 2023 at 6:20 pm
It cannot be omitted that this woman has a tremendously impressive ability to teach. She was able to walk a very wide range of people through the topic of infinity, adjusting the flow and terminology to the interlocutor, regardless of their age or degree. As a teacher myself, I can only offer my admiration and congratulations.
Johan Rama
March 29, 2023 at 11:34 pm
That’s the computer science brain thinking right there 😂
Biswajyoti Pradhan
March 30, 2023 at 12:47 am
Infinity my is nothing but…
We are lazy enough to count it.. Haha
Arielle
March 30, 2023 at 1:46 am
I live by this: if there are unlimited pieces of glitter, you need unlimited pieces of jar.
Willker Menezes da Rocha
March 30, 2023 at 9:45 am
The little girl is a genius
Don Pasquale
March 30, 2023 at 9:51 am
Didn’t know Tekkz was so smart
Aakash Kumar
March 30, 2023 at 11:13 am
I think there is no such thing as infinity. Every quantity is finite, we just need to find the way so that it can become finite.
Rakshit Ghildiyal
March 30, 2023 at 12:08 pm
Gojo fans- “Yes”
Boss Kaur
March 30, 2023 at 12:22 pm
wait…what method she told to count thoes spikes???
hi
March 30, 2023 at 12:26 pm
She’s 9, im 16 i dont think that critically when i was nine
WhyMe
March 30, 2023 at 12:30 pm
This guy looks like a girl
Xellius13
March 30, 2023 at 7:55 pm
Ok, one of my two working brain cells just commit suicide. Enough interwebs for today 😭
facu
March 30, 2023 at 9:13 pm
I understood the child level
Pratiksha Thakur
March 31, 2023 at 7:52 am
yeah i feel u girl my brain is exploading to
raechel
March 31, 2023 at 11:23 am
I lost her at the college student
Yourie Chooy
March 31, 2023 at 5:09 pm
If she ask me
What do you know about infinity
*me : stones 🗿
ICHIGO 007
March 31, 2023 at 7:09 pm
Love the haircut!
Der führer
March 31, 2023 at 7:09 pm
Love the haircut!
Lapota Junior
March 31, 2023 at 9:53 pm
Bruh so easy infinite is endless
Access Denied
April 1, 2023 at 4:35 am
Got lost after the kid lol
Rahul K
April 1, 2023 at 1:05 pm
They lost me after Undergrad. I guess I’m upto my level.
Diana Chan
April 1, 2023 at 2:34 pm
I’m lost at teen level! 😂😅
hbzdgaf
April 1, 2023 at 3:03 pm
math 2
Gennady Marchenko
April 1, 2023 at 4:04 pm
You’re finite, Zathras is finite.
preetpushap singh
April 1, 2023 at 11:10 pm
I can just say that, i love my mottu infinity.
backfaced
April 1, 2023 at 11:35 pm
How does she look 16 and 36 at the same time?
Precillia Soekhai
April 3, 2023 at 5:35 pm
She s Fire
Brian Garcia
April 2, 2023 at 1:29 am
Jesus is lord 😊
KingOfGamesss
April 2, 2023 at 3:54 am
Everything is ‘Existence’ & ‘Existence’ is Infinite…therefore everything is Infinite
Z Rizuki
April 2, 2023 at 4:05 am
gojo satoru should take notes
guilherme cavaco
April 2, 2023 at 4:38 pm
European school system >>>>>>
Terrence Ly
April 2, 2023 at 5:25 pm
N = Natural numbers, counting numbers = {1, 2, 3, 4….. }, W = Natural number and zero = {0, 1, 2, 3, 4, …..} Even a mathematician used these terms incorrectly, which is why so many students/people are so confused…
a – a => cancel = 0, x/x = cancel = 1…. but 0 is not 1, hence “cancel” is misused…
That’s my forever rant!
Good explanation of infinity though!
ExtravagantPanda
April 3, 2023 at 1:43 pm
There is no universally agreed upon definition of natural numbers in mathematics. Sometimes 0 is included, sometimes it isn’t.
My Adventures
April 2, 2023 at 8:17 pm
I thought infinity was a car.
Evan Cho
April 3, 2023 at 2:31 am
I love the sound of chalk on the board
manmeer gill
April 3, 2023 at 5:29 am
Everything up to level 3 is common knowledge due to channels like Vsauce getting into these concepts since as long as I could remember. I can’t tell if Vsauce taught it simpler or harder than this video.
Johnathon Tillman
April 3, 2023 at 5:44 am
I would love to talk to this lady all day
Precillia Soekhai
April 3, 2023 at 5:32 pm
She has to be my big sister❤❤
Alan Rice
April 3, 2023 at 8:47 am
I disagree with the speaker about integers and natural numbers being the same size infinite set. The integers are clearly a larger infinite set than the natural numbers. The fact that you can always find matching numbers for both sets is irrelevant. All natural numbers are integers but not all integers are natural numbers. Therefore, integers are a larger infinite set than natural numbers.
ExtravagantPanda
April 3, 2023 at 1:41 pm
The fact that you can always find matching numbers for both sets is not irrelevant, it is the literal definition of two sets having the same size. You can take issue with the mathematical definition, but you can’t deny that, in the mathematical context of this video, it is 100% factual to say that the set of integers and the set of natural numbers have the same size. Doing so is like saying 1+1 does not equal 2 because you don’t agree with the “standard” rules of addition.
John Wiltshire
April 3, 2023 at 9:39 am
There are notions that of late
I have come to often berate
I have no affinity
For that there infinity
It’s big, but it just isn’t great
I know that this could cause friction
With those who saver this fiction
But there is no infinity
In nature’s vicinity
We must rehab this insane addiction
Nothing goes on for ever and ever
Pretending it does just isn’t clever
Because we can trim it
We don’t need the limit
And connections to this we must sever
Let’s just say “Finity” and sow a seed
To do away with extension greed
Mathematics lumbers
With irrational numbers
But the rationals are all that we need
If as Mathematicians might well have feared
All irrational numbers just disappeared
Much as they might want-um.
Life stops at the quantum
Engineers and scientists? They cheered
If the fiction goes on to persist
And Mathematicians choose to resist
Seek fundamentals
With transcendentals
Because Infinity, does not, exist
WESLEYLEPRO
April 3, 2023 at 9:43 am
3535th comment
Precillia Soekhai
April 3, 2023 at 5:14 pm
Love this!!!
Precillia Soekhai
April 3, 2023 at 5:17 pm
Love this content ❤❤❤❤
Door Numb
April 5, 2023 at 12:41 am
Is the last part even a mathematician? Or just a philosopher?
Bending the wire
Hudan Bayu
April 5, 2023 at 3:52 am
where is for Level 0 ?😂
FREE MUSIC for YOU
April 5, 2023 at 5:05 am
Re phrasing Einstein I think that every infinity is relative to the “observer”
Ashish Upadhyay
April 5, 2023 at 6:09 am
Her ability to engage with such a wide variety of students on different level is incredible.
Esteban Outeiral Dias
April 5, 2023 at 5:31 pm
Sorry kiddo there is actually 4013 glitters but at least you tried
MrGreedylou
April 5, 2023 at 6:03 pm
Are they not just looking for binary answers to infinite problems? The answer to the existence of infinite spaces or sets could easily be and is : = cheese
Jorge Quiroz
April 5, 2023 at 9:38 pm
excelent explanation
Rubik Cube
April 6, 2023 at 11:23 am
Wow this is wild
Fabian
April 6, 2023 at 4:21 pm
math is cool
leahlynn
April 7, 2023 at 9:19 am
Math is cool
Matt
April 6, 2023 at 5:13 pm
that first girl is smarter than half the Americans I’ve come across.
Mark Gaskell
April 7, 2023 at 6:35 am
Great teacher
eavesdropper
April 7, 2023 at 8:05 am
Is this mathematician non binary?
TheRealBean
April 7, 2023 at 4:17 pm
I’m 13 and could understand up until level three.
MKWKezer
April 7, 2023 at 6:11 pm
Emily Riehl is the best! All of her books are amazing!
Hopefully this grad student now knows who she is and has at least read Category Theory in Context 😀 Or after this appearance he should start applying infinity-categories in algebraic geometry…
Miles Morra
April 8, 2023 at 2:48 am
Thought it was a little boy in a suit
Danny Mze
April 8, 2023 at 9:23 am
Yo who else thinks the mathematician is kinda hot? I think I’ma slide in her DMs.
caveman
April 8, 2023 at 11:02 am
What a waste of brain power. None of this stuff is relevant to real-world problems. They could be designing experiments in the sciences or working on artificial intelligence but they waste time with fantasy nonsense.
Riyadh Firdausy
April 8, 2023 at 11:22 am
17:20 means we can create something out of nothing v:
Jessie Marin Alfaro
April 8, 2023 at 7:10 pm
emily girl you looked so familiar… then i remembered that I did a presentation on you for my ap calc class in highschool.
Jon B
April 8, 2023 at 8:18 pm
But in reality it’s meaningless.
Allan M
April 8, 2023 at 9:54 pm
3 thousand comments- as a child, I had worries and nightmares of infinity. Anyone else? Maybe young minds are the key..
Chill
April 8, 2023 at 10:29 pm
As a puzzle game enthusiast the little girl saying “if you have an infinite piece of glitter you need an infinite piece of jar” gave me a ketamine induced flashback to Patrick’s parabox
J Burnett
April 9, 2023 at 12:38 am
hi Ren!
Dustin Platt
April 9, 2023 at 1:10 am
5 levels of infinity:
1. My bank account is infinitely at a negative balance.
2. My phone is infinitely low on battery
3. My choice of women is infinitely wrong in the instance that they are always psychotic.
4. My bank account balance is infinitely negative because of #3
5. Kill me… infinitely.
네펜데스의 꿀
April 9, 2023 at 9:21 pm
That child is smarter than me.
Stormer Games
April 9, 2023 at 9:52 pm
The child is smarter than most influencers today
Cupapet33
April 9, 2023 at 10:26 pm
i bet the kid can explain a better definition of gender than this goof
Alvaro1ization
April 10, 2023 at 7:44 am
A woman explaining maths, what a time to be alive lol
Marie
April 10, 2023 at 8:53 am
One of the things that caught me off-guard when a friend said it to me, was „some infinities are bigger than others“. Like WHAT? But it makes sense. There is an infinite number of whole numbers (or what do you call them? Like 1, 2, 3, 4, etc). But there is an even bigger infinity of decimals like 1,1 ; 1,2 ; etc.
ExtravagantPanda
April 10, 2023 at 10:48 am
That’s a bit misleading. It’s true that some “infinities” (i.e. infinite sets) are larger than others, but if you’re talking about integers and decimals, it’s specifically the “real” numbers (or just the irrational numbers) that is larger, i.e. decimals with infinitely many digits. The integers are actually exactly the same size as the set of rational numbers (decimals with only finitely many digits or infinitely many repeating digits, e.g. 1.1 or 1.11111111…). It’s very unintuitive.
Marie
April 10, 2023 at 11:12 am
@ExtravagantPanda you’re right, I didn’t think about that
RadioBreaker
April 10, 2023 at 6:39 pm
Looks like the version of Katy Perry who learned that math is related to science
Juan Pablo
April 10, 2023 at 6:45 pm
🤯
Kiley Roy
April 13, 2023 at 10:58 am
If only my teachers explained things this well
Ally_Lynch
April 14, 2023 at 7:49 am
So there is a finite way to make infinity ?
nazart
April 14, 2023 at 10:17 pm
I got lost in the phd section, but totally understood the philosophic section
Mateusz
April 15, 2023 at 11:06 am
I think it’s stupid, doing science just for doing science. Infinity doesn’t exist in the nature, the infinite hotel doesn’t exist. If they admit it’s abstract, like poetry, and mathematics foundations are made up by them, why do they teach it their students? You don’t “teach” students poems because it’s just one way of expression, nothing universal. Why do they keep digging? For what?
Tomas
April 17, 2023 at 8:15 am
It’s quite common in mathematics to research some seemingly meaningless abstract concept and to find a useful application for it years later. Understanding infinite sets is quite important to formalize many areas of mathematics. A good example is calculus and that’s a very powerful tool
K3
April 15, 2023 at 12:06 pm
She is really good! A lot of professors should take a notice.
KhmerKIDOfficial
April 15, 2023 at 3:31 pm
Infinity is something that goes on for ever, not something that goes in circles. A circle is insanity looping and expecting different infinite results.
thelonewolf191
April 15, 2023 at 10:29 pm
Wait, chalkboards still exist???
Tertullian of Chicago
April 15, 2023 at 11:09 pm
This….this sounds more like philosophy
Kyle Petersen
April 17, 2023 at 10:37 pm
so infinity is infinite that’s so not that crazy
Lajusa
April 18, 2023 at 9:00 am
This woman is beautiful.
Maloosoy Katwa
April 19, 2023 at 2:27 pm
Every doctor, or social worker needs to master this skill of explaining in levels of difficulty, and weirdly, level 1 is always the hardest
David Whitman
April 19, 2023 at 5:32 pm
Infinity within the limits of… – this helps to describe the different sizes of infinity. I see this as way of saying more able to be comprehended than merely a size of infinity. Setting a scope in which infinity can be infinite, for instance, infinity in x direction starting at y point.
Bonolio
April 20, 2023 at 5:50 am
Does 2 x ∞ = ∞
Chiang Wey Tan
April 20, 2023 at 9:16 am
That young child has a talent. Her intuition is impressive for that age.
Fundu Bits
April 20, 2023 at 10:30 am
Why don’t I hear the simplest explanation…. ” Ininity is a number that takes you out of context ”
While doing calculations at atomic scale, 1cm is infinitely big.
While doing calculations at cosmic scale, 1cm is infinitely small.
100000000000000000000 is infinitely many skittles
100000000000000000000 is lesser than the number of stars in the universe
Sammy Wauneka 3
April 20, 2023 at 10:57 am
How about infinity in smaller numbers like irrational fractions
Mahesh
April 20, 2023 at 11:12 am
Can infinity get bigger😮 How can a child think of such a deep question. She is really smart
Mostafizur Rahman
April 20, 2023 at 5:38 pm
Why did you skip her explanations? I was trying to understand.
DaniDhyana
April 21, 2023 at 12:24 am
Infinity is pretty easy to comprehend. It is a concept, and idea, but it isn’t a number since there is always a number bigger than the previous, or smaller.
DaniDhyana
April 21, 2023 at 12:30 am
I think this has some flawed explanation. Infinity is not a number, it is a concept. Infinity can’t be a number because it is Infinitely large, so you can not add to it or multifunction or divide or anything like that. Duh.
R Garlin
April 22, 2023 at 5:09 am
Infinitely interesting and infinitely amazing to me…
gefoghilergu
April 22, 2023 at 3:54 pm
✨unlimited peices of jar✨
Chris Kelly
April 22, 2023 at 6:56 pm
it’s turns out that despite asking guests to arbitrarily swap rooms multiple times, and all the plumbing issues, the hilbert hotel chain has been around long enough to rival most hotel chains
Chris Kelly
April 22, 2023 at 7:10 pm
i love that the answer to the question of ‘how can this be used in a practical way’ was met with a wildly impractical idea about what a non existent machine might be able to do. Mathematicians, you are weird and i’m here for it 🙂
Chris Kelly
April 22, 2023 at 7:14 pm
the issue with trying to consume these ideas is that beyond the 16min mark, there’s too much jargon being used to describe other jargon that they aren’t really explaining infinity fully anymore… to understand what’s being described, you already need to know all the terms. to know infinity, you already need to know infinity…i guess i shouldn’t be surprised
alkaline
April 24, 2023 at 4:41 am
Man all the people who came were so smart, my brain woul’ve been frozen
Miha Leben
April 24, 2023 at 8:04 am
Limits, thats the thing.
witch of marchengast
April 24, 2023 at 8:57 am
I love how every time we reach Experts stage, there’s no teaching or educating done, just discussion and sharing of thoughts and ideas.
Vikas Singh Bisht
April 24, 2023 at 10:52 am
Can somebody explain why there is ‘0’ in natural numbers?
ExtravagantPanda
April 24, 2023 at 2:28 pm
There is no universally agreed upon definition of the natural numbers, sometimes 0 is included, sometimes it isn’t.
Vikas Singh Bisht
April 28, 2023 at 3:46 am
Oki☺️
Neon Black
April 24, 2023 at 1:19 pm
I feel like the 3rd guy was already all over the stuff she was talking about…. but then the last 2 I had no idea what language they were speaking anymore
Neon Black
April 24, 2023 at 1:32 pm
wish I got to hear more of the “experts” opinion at the end but great video!
fogfrog72
April 24, 2023 at 9:22 pm
Jeremiah 29:11 ~ For I know the plans I have for you, declares the Lord, plans for welfare and not for evil, to give you a future and a hope.
BennyX
April 24, 2023 at 9:35 pm
1:40 unlimited pieces of jar 😂
Mani Babai
April 25, 2023 at 7:31 am
I’m just amazed by her ability to teach ! She breaks down the topic so beautifully considering their age and level of studies without a single pause ! I wish I had a professor like you ! What an amazing person!
It's just me
April 25, 2023 at 7:44 am
remind me never to stay at hilbert’s hotel. once im in my room i aint moving for anyone!
Tankiso Bosiu
April 27, 2023 at 2:48 am
This kid is like really really smart like realistically that’s what a genius child thinks like.
Ondy
April 27, 2023 at 8:39 am
“Finite distance away” – omg imagine being in room 10,000. And the diagram shows that it’s just infinitely narrow and horizontal meaning the only way out or in is to walk the path. Absolutely a 5 star hotel for mathematicians, -5 star hotel for design
MTalha
April 27, 2023 at 10:54 am
Emily Riehl speaks fast just like my mathematics professor, except she speaks clearly. ➕️➗️➖️
dheeraj upadhya
April 28, 2023 at 12:13 am
Daniel Dubov is a mathematician?
E A S O N
April 28, 2023 at 3:03 am
she lost me at the teen
Reece Herman
April 28, 2023 at 10:38 am
One time I was teaching some first graders about the concept of infinity with 2 other highschool seniors for a pi night thing for our math honors society. One of the girls I was working with told them that there is nothing bigger than infinity. After we finished our presentation and were getting ready to leave, a little first grade boy came up to me and asked about omega plus infinity. Absolutely baffled me that he has so much as heard of that.
Robert Nunez
April 28, 2023 at 1:47 pm
I still don’t understand how you can manipulate a concept like infinity like you can a number. Infinity is not a number. It’s a concept. How can you add two infinities…. if by infinite you mean everything? If by infinity you mean EVERYTHING then you couldn’t possibly have two infinities in the first place. One would subsume the other, right? Because if you have two separate infinities then you didn’t have one in the first place. What am I missing here?
ExtravagantPanda
April 29, 2023 at 11:23 am
Infinite does not mean “everything”. In this context it simply means an infinite set, i.e. a set that does not have a finite number of members, such as the set of all positive integers {1, 2, 3, …} or the set of all integer multiples of 3: {0, 3, -3, 6, -6, …}. Both of these sets are infinite but are clearly different sets; there’s nothing wrong with “having” two infinite sets at the same time.
And you cannot add infinity or do any other arithmetic operations with it (not typically anyway, though sometimes in math the real numbers are extended to include infinity, but you have to explicitly define what it means to add/subtract/etc.). They weren’t being very rigorous in this explanation when they said that infinity * 2 = infinity. Really what they should have said is that, if A and B are infinite sets of the same “cardinality” (the same size, basically), then the union of A and B (analogous to A + B) is also an infinite set of that same cardinality.
royed31
April 28, 2023 at 1:50 pm
She talks to herself
einrazer
April 28, 2023 at 2:30 pm
I’m not saying that it isn’t a good explanation. But the child clearly already has a strong grasp on terminology and concepts beyond those of her age in my experience. I teach high school math and kids much older than her could not answer these questions without more guidance.
Andre Matarazzo
April 28, 2023 at 4:25 pm
I got lost at the teenage level. Maybe I’m infinitely stupid.
Guilherme Gomes
April 28, 2023 at 7:21 pm
basically its more about philosophy than math
Gavin Fillop
April 28, 2023 at 8:06 pm
Doubt
sinohui3
April 28, 2023 at 8:17 pm
Weird. And fascinating.
David Albro
April 29, 2023 at 11:02 am
6th level of understanding
Infinity has interesting characteristics, but infinity cannot be understood conceptually directly because concepts, by definition, are finite. These interesting characteristics of infinity are just that: characteristics of infinity but not infinity itself. Only the infinite can know the infinite.
Thoughts are concepts. Concepts limit. Concepts tell us what something isn’t. They are an attempt to break down reality into what it is not in order to understand what it is, but by understand what something isn’t cannot get us fully to what something is. It can give us a better understanding of what it is, but can never, by definition, give us a direct experience of it.
In order to understand infinity you have to release all thoughts and concepts. This can be done through mindful meditation. While it may take some practice, millions of infinite consciousnesses localized in human forms, aka humans, have known infinity.
You can, too.
Daniel Cintz
April 29, 2023 at 7:12 pm
8:25 contreversial putting 0 as a natural number there lol
ben benazzi
April 29, 2023 at 8:33 pm
Agreed.
Ray White
April 29, 2023 at 9:04 pm
I want to have a kid now, just for the chance I get 1 like that first girl.
Joey Salazar
April 29, 2023 at 10:28 pm
xx≠xy
Moopi Boopi
April 30, 2023 at 12:09 am
i could listen to Emily all day, holy moly. so interesting! i love these kind of deep topics.
Cory_from_Cordesville
April 30, 2023 at 6:51 am
Why the woke woman
gamer480
April 30, 2023 at 8:27 am
Everything we know is a grain of sand.
Omar Hernandez
April 30, 2023 at 1:31 pm
If infinity is the universe and the universe as a whole equals mathematics as the numbers that follow up the next be it fibonacci sequence or reciprocal in decimal there is virtually nothing too big, bigger or biggest/small, smaller or smallest to name in words.
Mr. Simplicity And The Simplicity Lifestyle
April 30, 2023 at 4:58 pm
It’s just as hard to imagine the Universe as being finite as infinite.
Aborted Democrat
April 30, 2023 at 8:17 pm
Is this person a man woman or mistake 🤔
Scott Macdonald
April 30, 2023 at 11:21 pm
I was hoping this was going to wrinkle my brain, but unfortunately, my brain remains as smooth as a egg.
Whasgewd
May 1, 2023 at 2:17 am
I have a math degree and I wish she was one of my past professors
bOt25X
May 1, 2023 at 2:18 pm
She is Smart and She is Beautiful.
PIPED UP
May 1, 2023 at 6:40 pm
“We need unlimited pieces of jar”
I mean beautiful mathematics
Timothy Campbell
May 1, 2023 at 10:40 pm
🫨🫨
Frank N
May 2, 2023 at 12:06 am
You can fill empty space completely with just circles without overlapping… would experiencing that might come across as … inflation / dark energy? :]
0xvenezuela
May 2, 2023 at 2:47 am
I had a girlfriend that looked like her and thinked like her… Infinite pls help
Cesar Omiste
May 2, 2023 at 3:03 am
Great discussion covering all the interesting branches of mathematics that must contend with concept of infinity.
The Science Of Gambling
May 2, 2023 at 6:59 am
there is something I still don’t understand about Cantor’s theorem
you said you can create this new number
but so what ?
then this new number we add to the list
so this process of creating new numbers which weren’t in the list yet, just keeps on going forever
nothing more
but that doesn’t mean it’s not in the list
it just means that this process of creating new numbers never stops
but this is the same for numbers
if I ask you give me the digits Pi consists of … it also will take you forever to telling me what exactly pi is
here this creation of new numbers lasts forever
I see no difference
where is the difference ??
pakuszka
May 2, 2023 at 2:24 pm
I disagree on concept of the infinite numbers of infinities of different cardinalities. The infinity is only one. Also if we listed all numbers between 0 and 1, there would be no room to find a new number not already listed.
@stack_of_records
May 2, 2023 at 5:00 pm
Infinity is growing. To something really large or really small. No limit.
Like the universe.
It is an approximation.
Hockey in Alabama
May 2, 2023 at 6:30 pm
How is it that I understood the grad level explanation better than the college?
Hoang An Nguyen
May 2, 2023 at 7:40 pm
Saroru Gojo watches this for his techniques
sleepn_on_me247
May 2, 2023 at 9:01 pm
Philosophy is the great engine of hypothesis
sleepn_on_me247
May 2, 2023 at 9:03 pm
Gottfried wilhelm leibniz
David humes
Immanuel Kant
Your welcome