but negatives :( -1 -10 -100 -1000

@@Tevin-MK Also true for negatives though because -1 is "bigger" than -2...

I said this about space. If the universe is infinite but only 13.77billion years old. Holy smokes are we young! We might actually be the first species! Fermi paradox solved. Goodnight.

@@masonfarnsworth6730 lmao

Nah what about the number infinity divided by 2 plus 1. That's close to infin6 Lmfao

I know, right? it's terrible

except nobel prizes aren't awarded post mortem of after death. For examppe Ghandi died the year he would've gotten a Nobel Peace Prize so that year no prize was given out at all.

Alex Chuoy Sorry, I don't understand what you mean by "post mortem of after death". As for your example, it's kind of similar to what I said, because in the end, Gandhi never knew about the honor he received.

Anyar oops its post mortem OR after death. Ghandi didnt get the Nobel Peace Prize because he was dead. One of the rules is that you have to be alive to be awarded the prize.

Alex Chuoy Oh, okay. My bad. For some reason, I seem to remember hearing about Nobel prizes being awarded to people long after they've died. Weird. My memory has failed me.

Yes

Does understanding this reference make me a nerd?

Men: hmm yes IS the floor here made out of floor ?

I remember it too

Yep

We even have a shloka in Hinduism like that

"Purnasya purnamaadaaya purnaavashishyate "🙏🙏

True

This works for every number.

Well yes but actually no but also yes It only works with "infinity" Infinity - infinity • Infinity = 0 X - X • X = X

I am a school student and I'm glad that I got the opportunity to learn these thing at a young age.

@@MarkWatney You learned nothing, except that some people intentionally corrupt mathematics

O hristiyan işareti bu müslüman dua işareti 🤲🏻

@@abdulkadiryukselking so wht

Limitless !

ah you small joke cokkie

I broke the rules,look! Omega,omega+1...

It is as well infinitely small

Your mind is having a good time

It makes sense

My mind is struggling 🤦🏾‍♀️

Infinity is piling up in your brain

Ok

+Lugmillord No if i list the infinity of negative numbers

+Guilherme Medeiros Just because the set is of negative numbers, the cardinality isn't going to be negative... fail XP

+Lugmillord Hint: Smaller than infinity+1 Oh wait...

Hint: Bigger than 245355354243134143243654655746547658758756756544243143654765765764675764764664654754.... I think you get the point

YOU'RE GONNA HAVE TO DO BETTER THAN FIVE

Cesar Escobedo But what if you think matematics as a human convention?

Human built mathematics, which had them confined to understanding. :P

Actually Godel literally proved that there can't be both consistency and completeness of axiomatic systems at the same time. Therefore all mathematical logical systems have some unprovable statements

Mathematics IS we If we have limitations, math has them too (I'm not an english speaker, my grammer can be bad)

problem: mathematics is bound to whatever container our reality is in. like, our reality follows maths, some other reality could too, but there must be other realities which don't. but, to be honest, such "reality" does not "exist" same way as ours, so it can never be discovered.

That's because it doesn't make sense. It's contradictory in it of itself.

Are there any aspects of it you're still struggling with? Perhaps I can help address some of them.

@@MuffinsAPlenty Yes, please address how one infinity is bigger than another infinity. I understand the concept of cardinality, so no need to go there.

@@wade5941 Cardinality is what people mean when they talk about some infinities being bigger than others. Ultimately, it's a generalization of how one thinks of sizes for finite sets. Are you looking for an explanation of why "size" is a good descriptor for cardinality?

@@MuffinsAPlenty Infinity is unbounded space, time, and quantity. Again, I understand that one specified infinity can have more elements than another specified infinity. Even though the one infinity has more elements than the other, they are both still "unbounded" and infinite. I understand that one infinity can be a subset of another infinity, but both would still be infinite. I think my struggle is why does cardinality even matter when it comes to the concept of "infinity". I understand why it matters in the world of mathematics. I suspect I am making this harder than it needs to be, so will understand if you move on.

Remember me when your comment get popular

Ayasha no

Our earth itself is pretty damn big. Infinite has no limits.

Remember me too :( I am one of the intellectuals that understood this video before you simplified it

Ok

I guess Some infinities are faster than others and Not bigger.

+Cinichecuk I gues some infinities are just more handsome than others

+Cinichecuk I guess you 're watching too much The Fault of Ours Stars

+Cinichecuk looking for this

They'd have to be finite then. 1 is actually bigger than 9 Because of: 9 10 The 9 is to the 1 there is no number to "the zero"

Graham's number?

Actually infinity is a concept of how number dont stop

INDOMTM4X r/whooosh

not realy just imagine that 3 is the biggest number i can think of and -3 is the smallest i add them and it gives 0 so is 0=infinty?

armando valente r/whooosh buddy.

+

Indeed, infinitely many infinities are bigger than infinitely many other infinities, e.g., the infinity of all real numbers is bigger than the infinity of all whole numbers and the infinity of all the subset of real numbers is bigger than the infinity of all real numbers and so on and so on.

Abhipsha Sahu Infinite is infinite not a number just unlimited no limits

@Michael OchoaRomero wrong

Multifinity is bigger and smaller than Omnifinity

MEME: becuase a prezel is infinity

♾ Is ♾ times bigger than: 84846473838383746467373837374637288373646373737373736736737373635363737373763637282837377363647473737373736378292918283783929101010101001928374746287373638393983837373737383838292929387312 to the power of 84846473838383746467373837374637288373646373737373736736737373635363737373763637282837377363647473737373736378292918283783929101010101001928374746287373638393983837373737383838292929387312 to the power of 928383836636372727377383837384859595959949448474288229827364728929282837373746474747838292910018273635436637373738839393939939393! (! Means factorial, for example A factorial means all positive numbers smaller and A itself multiplied with eachother for example 4! Is 24

🥨 :)?

Its pink. Looks a bit moldy

@@paulneamtu1373 wrong lol

That read more’s fake😂😂🤣

Ye but how ... is that even possible?

jr.akuchi Dre if the “read more” is fake, i wouldnt see the chinese text. (im using the chinese version of youtube)

Ok

B

I'm sacred

I'm terrified :c lol

Flurry Heart I’m 4 months late but I like you.

I'm scared I won't finish detective Conan in my lifetime

Nothing to scare... -_-

My grades varied hugely depending on who was teaching. This does in fact make a huge difference and I have to say that when I learned our main maths teacher died in his 50s I did not exactly shed many tears...

If you worked harder you'd have better grades. People always blaming others for their own failures.

@@petergianakopoulos4926 that's true, it's also true that if I taught myself all the maths at home from books and the internet I would have better grades, but the point is the teacher is there for a reason

@@petergianakopoulos4926 the work you put in and the quality of teachers both make a difference. You can't substitute one for another. A good teacher alone wouldn't get you good grades, neither would just hard work.

Yeah you would do better in philosophy math, this video isn't about the academic one.

Yeah I understand the joy behind that pain. I, most of the time do not completely understand such videos but I feel good after watching them.

Apeirophobia?

??????????????????????????????????????????.

No!

And you are drugs METH!

magicstix0r nope math is not drunk

@@weirdgaming996 r/whooosh

y'a nkown 3.14=1NFYN1TY

Nataly RAW lol

Nataly RAW youre blonde right? lol

islezeus nope, and it's you're*

islezeus come on then

Nataly RAW what a jenny ass

To face the fear and render it to dust spilling from the palm of your hand?

So that is to say... you are afraid of infinte things?

Oddly enough, his explanation of the fact was wrong.

that bc john green sux

Vi Hart gives a nice explanation

***** Take a moment to watch the video. It suggests a very natural measure by which you can compare two infinities.

well said! i

There are many mathematical conjectures that can't be solved.

You should've paid more attention in school then

@@mohadams3754 I actually do pay attention, I'm a good student with good grades, they just don't teach useful stuff at all and just stress me out.

It is not possible to know everything there is about mathematics, because it is said in the video that there are questions that can't be answered, so you don't know if something is this or that, thus you don't know everything about mathematics

That's where weed comes in, my man. As it does for me, it'll show you some really interesting concepts such as hyperinfinity that's pretty much like this video. Mind you, not every strain can get you to do this.

Kurt Godel proved that in any logical system capable of modeling basic arithmetic, you can create statements that cannot be proven or disproven. (He actually used Cantor's diagonal argument presented in the video!)

M_ Vanvid yeahh!! Buzz Lightyear

Infinity😂

Buzz lightyear

palmomki

Damienation Animations

Yes, but try explain ZF(C) to "common people". It may seem "easy", but Skolem's paradox shatters everything. So you need some intuition, and the easiest way is to "accept" ZF(C)

I do believe you're right

IF YOU GUYS FEEL SMART ENOUGH TO SOLVE CONTINUUM HYPOTHESIS POST YOUR PAPER HERE, THERE ARE FAMOUS MATHEMATICIANS like Terence Tao, John Conway, etc michaelnielsen.org/polymath1/index.php?title=Main_Page

I agree

Underestimated comment

One basic axiom would be 1+1 = 2?

@@kevinsantillans7415 It could be, but in ZF based math there's no need: 1+1=2 is actually already something you construct out of other things rather than a basic axiom. The ZF axioms are things like "if two sets contain the same elements, they're actually the same set", "if you have two sets x and y, there also exists a set z made up of the elements of both x and y" and so on. To get to 1+1=2 from there, you go "let's call {[set of sets constructed in a specific manner]} a set of Integers: {0, 1, 2, 3, ...}, and let + stand for a specific set operation". You can then show that when you define numbers and addition as such ("numbers actually stand for specific sets" and "addition stands for a special operation on those sets"), it works exactly as expected. So, 1+1 = 2, but also 2+2 = 4, 5+9 = 14 and the rest.

Omega

*infinity+1...*

Something like "infinity+1" does actually exist within the ordinals.

infinity +infinity

Infinity*Infinity

tochoXK3 yeah omega+1

NEIN!

No. Infinity is between twelve and thirteen.

Water Spray 12.5 = infinity confirmed

Ryan S. Don’t you mean... infinnati

thats nine

Math has limits, science is still OK

@@agimasoschandir true, this world isn't made from math. It's created with the law of physics, math is there only to help in describing it.

@@That_One_Guy... agreedddd

+Fez Master And what goes beyond infinity?

***** Nothing. Infinity is a fake concept that goes on forever. But, since it does go on forever, you can never equal it.

Well what goes beyond infinity isn't nothing. Instead it is again infinity. Meaning if you had infinity plus infinity times infinity you get infinity. However if you have infinity divided by infinity^2 you get 0 because the rate that infinity reaches infinity is much faster on the denominator. #calculus

+Jason Hong but, they had said that there are many infinities. Maybe infinitely many infinites hshsh

+Fez Master If you want to know how big infinity is, just think of an unimaginatively incomprehensibly huge number to represent infinity, and realize that that number is precisely as far from infinity on the number line as is the number 1.

P

@@SEBithehiper945 NP

+SamThe RandomG1rl and boy does it! ;)

Sammy Dreemurr you can try to be the first person that can harness nuclear fusion energy.

in case you do it remember i believed in you before anyone else sammy dreemurr

damn bro that was actually hilarious

Nope, that's 30 million blocks

Not really bro. Minecraft will either stop on its limits (roughly around 30 million blocks), eventually render an already existing chunk, or if you remove its limitation, stop when it completely fries your computer.

Minecraft is 8x bigger than Earth which is not infinite

What y'all say is true, but that was my first thought, because Minecraft is practically infinite and that's awesome -3-

Wait. 8 flipped to right = infinity

🅱

Exactly! As soon as we say an infinity is bigger than another we are measuring infinities. If we can measure an infinity then it is not an infinity at all!

***** Actually it's really easy: infinity is not a measurment of size, it's an idea, and that's why regular laws of math don't affect it (you can read a little about it's usage in infinitesimal calculus and set theory - which are entirely different, but in their fundemental concepts are very similar). Since infinity is not a measurement of size, quantity or length, when we say one infinity is "bigger" than the other, we do not mean it is bigger in size, but bigger in the way that WE grasp it. The claim that the real numbers' infinity is greater than the rationals' comes from the idea that you can find a method to count all the rationals in the world (even if not in practice, then in theory) - but you cannot find any method to count all the REAL numbers, not even in theory - and that's what Cantor has proven using the method shown in this video (called Cantor's diagonal argument).

Imaging there will be an endless race of 2 straight lines going with the same speed. 1 line goes first. That one will always stay longer the the other one. Though they are infinitely long.

did you watch the video?

James Jones Technically plunger is right. There is a difference between the size of an infinity ( which is nonsense ) and the size of an infinite set - otherwise known as a carnality. This video glosses over the distinction in the very first couple of minutes and the term has been used incorrectly again and again.

there's nothing to understand here buddy

Spoken like someone who's good with numbers... Check your privilege@@applecider9630 😜

Check out the video by Vsauce called how to count past infinity. After that try reading Naive Set Theory by Paul Halmos. After that try learning some ZFC set theory. Most importantly, take good notes, and remember to have fun.

@@anishia i just think we will never have a theory that explains everything, there will always be something we won't understand

Adam Crume The one that stole my brain's lunch money.

Adam Crume Good question, but you can actually prove that there is no "set" of all infinities

infinity.

actually there is no infinity. That's just a myth. the only true thing is - ILLUMINITY

its a class not a set

Favourite and valid quote

A sketch of the workaround: There are in fact -precisely- at most two representations of each rational number by decimals, one terminating (i.e. an infinite string of zeroes), one non-terminating (an infinite string of 9s as we're in base 10) (EDIT: see my next comment for fix); and precisely one representation of an irrational number by a decimal. We can always take the representation of the rational numbers by non-terminating decimals, hence get unique representation.

David Roberts so how does 1/3 match your workaround? The statement must be weaker: only allow sequences that do not end in an infinite sequence of 9s. Then the decimal representation is unique (I do not prove that, but it's not hard to see). Also take care that the decimal sequence you construct to be not in a given list does not end with an infinite sequence of 9s, but that's trivially possible.

***** >:-( stupid me. I would still say the same, but say that _either_ there are two decimal representations (as above), or there is a unique representation. And, in building the number not on the list, don't use 0s or 9s, so the number you build corresponds to a real with a unique decimal representation.

This problem is discussed in the book An Introduction to Mathematical Reasoning by Peter Eccles (p. 177). He notes: "Some numbers (such as 1.000... = 0.999...) have two decimal expansions, one ending in recurring 0's (and so a finite decimal), and one ending in recurring 9's. For these we always use the first representation."

Robert Jacobson Thanks for the reference!

Me : bigger than 8 Mafs ...

+Justin Barker You should always be very critical of your arguments in mathematics, you can easily trick yourself into believing something that is not true at all. For each subset of N, there should be a corresponding number in N for your argument to work out. Now N is obviously a subset of N, so try to think of a number in N that corresponds to N itself in your list.

I obviously forgot about infinitely large subsets... *facepalm*

Nope

Ah, maybe try watching it again?

I understood it perfectly and I'm a casual 14 year old. Maybe try watching it again but paying closer attention, although your comment is form a month ago so you probably already did that or don't care anymore.

Well, the simple fact of the matter is that human brains cannot understand infinity. You have to let go of everything but pure mathematical reasoning, or else it won't make sense.

Aleph-0 is the cardinality of the set of all natural numbers. (In fact this is usually realized in set theory as the set of natural numbers itself.) Aleph-1 is by definition the next higher cardinality. Without additional axioms, we don't know what is exactly the cardinality of real numbers; it may be aleph-1, aleph-2, aleph-3, and so on. (It can't be aleph-ω=aleph-(aleph-0); but it can be greater than that.) In absence of axiom of choice, it may be even the case that real numbers can't be well-ordered, in which case their cardinality is not an aleph number at all. It can be shown that given any well-ordered set, there is one with strictly greater cardinality. For simplicity, take the set of all natural numbers. Now consider the set of all well-ordering relations on natural numbers. Each such relation has an order type equal to some countably infinite ordinal number. Take the union of all these ordinals. The union is still an ordinal, but it can't be countable (on the other hand, every its element is countable), so let's label its cardinality "aleph-1". (Under the usual definition of cardinal numbers, this ordinal number is the same set as aleph-1.) The same can be done with any well-ordered set. (If the set X can't be well-ordered, then we can change the procedure to get the set of order types of well-ordering relations on subsets of X. There is no well-ordered set with strictly greater cardinality than X; but this yields the smallest well-ordered set whose cardinality is incomparable with X; any smaller one has a strictly lesser cardinality than X.) See the Wikipedia article "Hartogs number".

I totally agree. In fact, I stopped watching because of it.

I found it terribly disgusting too.

oh my god i thought i was the only one! the lip smacking irritates me so much!!

He's probably using an electrostatic microphone or a ribbon microphone which capture these kind of soft sounds much better than more common mics (electrodynamic), coupled with the fact that he must have had moist lips and tongue while speaking this day (maybe he should have speak louder and drink more water..?) By the way, it irritates me too haha

Misophonia

Big brain🤪

Take X = the set of all natural numbers. Y = the set of all natural numbers divisible by 4. Y can be mapped one-to-one with a strict subset of X; for example, using the function y -> y/2 (this yields the set of all numbers divisible by 2) - a constant function would have worked as well. On the other hand, X can be mapped one-to-one with a strict subset of Y, e.g. using the function x -> 8*x (this yields a set of all numbers divisible by 8). There's a well-known theorem: if X can be mapped one-to-one with a subset of Y, and Y with a subset of X, then the two sets have the same cardinality - there exists a one-to-one function between them. (And indeed, our set X can be mapped one-to-one with Y - the mapping function is x -> 4*x.) There's one more result: a set can be mapped one-to-one with its strict superset or subset, if and only if it has a countably infinite subset. Assuming axiom of choice, this is true for all infinite sets.