The Banach–Tarski Paradox

I don’t get the difference between uncountable infinity and countable infinity… can someone explain?

And thats how they’re making chocolate bars smaller,you don’t realise until one day you buy a chocolate bar and you realise you have been ripped off

Inspirational

I would hate to stay in that motel 😅

This is silly and obvious.

But in the rules he told in the colour points you are just keeping the same colour adding to every point on the sphere then why there will be a differenciation and addition from it 😂😂😂😂😂

Seventh time spread out over a year, you still lose me at “Hey, vsauce”

Nobody:
Vsauce: Real life duplication glitch that hasnt been patched yet

Would there be an infinite alphabet of words though? I feel like if A, AA, AAA…went on for infinity, you’d never get to AB…
It would have to be its own set of infinite letters, and so on through the alphabet. 🧐

"1 + 1 = 1"

– Michael Stevins, 2015

What an utterly worthless exercise in mental mast**bation. He uses dishonest examples to fool the viewer. Chocolate bars, cash bills, dictionaries and hotels exist in reality. They are defined, we can measure their weight, length, etc. Infinite numbers do not exist in reality. Only the concept of them. There is nowhere that “contains” a list of “all” possible numbers. There is only the simple algorithm used to come up with another number.

This is exactly like the difference between bitmap graphics on a computer vs vector graphics. Any discussion about the absolute length of a line in a vector graphic is invalid. Only the length relative to the other lengths, and/or some arbitrary initial starting size.

I’m shocked Vsauce wasted our time with this video when his others are so good. Every idea he discusses in this video is invalid because it relies upon fooling the viewer into thinking infinite numbers are somehow finite. He uses all phony examples, because there are no “real” examples.

Nobody cares about a wallet that “could” contain unlimited cash in your imagination. It’s not even making a valid statement. It’s nonsense. The idea of “infinite money” is invalid because money itself is a thing whose definition and existence is entirely predicated upon it being finite. Even fiat currency can be counted, there is no cash bill printing press that has printed “infinite” bills. We can count every one. There’s an absolute limit, an upper bounds to the number of bills that could ever conceivably be produced just knowing the volume of the entire Earth containing the raw materials from which they would be produced.

It’s embarrassing reading all the comments from people utterly bamboozled into thinking some great profound idea has been revealed in this video. I can’t believe anybody even calls this a “theorem” or that someone actually spent time giving it a name. How pointless! I can’t believe “mathematicians” get paid to ponder such stupid bullshit.

1:31 could have given it to me

1:32 Mr. Krabs just woke up in a cold sweat

Thats just multi factoral . Eg 52!

IS THIA AN UNSERSTALE REFERSNXS?????

But every point has been counted more than once so you are not creating something new but counting it multiple times

Is this mitosis

Bruh i have an exam tomorrow dont mess with my sanity 😭
I swear i was understanding everything like until the sphere thing appeared and then un-understood everything 😭

10:37 yeah it would be huge, you could even say it would be massive

how is counting natural numbers something that can be done in a finite period of time, but real numbers isn't? we're able to count either, one just comprises of separate infinities between natural numbers. Arguably, there is as much infinity in between 0.1 and 0.2 as there is between 1 and 2. Just as such, can't you say there is as much infinity between 0.00000000001 and 0.00000000002? Like how is one infinity 'countable' and one isn't? Is it because when you go to count an 'uncountable' infinity, you will not be able to start in the first place, because there is infinite space between 0 and the next real number?

also, with the diagonal theory. say you line up the infinity of whole numbers with the infinity of real numbers between zero and one. you use the diagonal theory to create a new number not yet in the set. And then you count one more number upwards on the whole number set…
right? isn't the diagonal theory flawed?

also with the hotel thing… understanding infinity as unexpanding. If infinity is a concept described as akin to a number such as seventeen or one billion (each of these two being unexpanding), then infinity is also logically unexpanding. While this term is impossible to understand, and paradoxical, we can somewhat work with this logic. With an infinite number of rooms, all being occupied, we assume that this unexpanding concept or 'number', as one often thinks of it, of rooms has one corresponding guest. Now along with this, if we think of infinity as definite, as something that if manipulated will no longer be the same (like how when you do 17-1, the answer is 16, not 17), we realize the flaw in this logic that you could fit another person into the hotel. By working on the assumption that you can add or subtract (or otherwise manipulate) a theoretically pure 'infinite' set, and that you will be left with something indiscernable from the original, you in turn are treating the infinite set as finite; manipulable. This logic can also be applied to a situation when a guest leaves the hotel. Because you are treating infinity as a finite manipulable set, then there will logically be one room vacant. So I think this hotel problem is based off of conflicting definitions. There is infinity as infinity, and infinity as an infinitely large finite set. I believe those two have a difference.

The concept of infinity is inherently impossible to define or quantify, because to define or quantify infinity is paradox to what infinity is. Infinity is like a word in a language that has no direct translation into another language. Infinity belongs to the language of the unexperiencable, and the aspects of existence that humans interact with and were designed to exist in, are of the language of the experiencable (I thought of saying language of theory, and language of reality, but theory is indistinguishable from reality)

So this video treats the concept of infinity under the definition of an infinitely vast finite set. Another comment, when you begin an attempt in understanding the impossible, you see the same thing. Almost like in quantum superposition and other things. When you go so small, or so big, things no longer exist. because to exist (to us humans) is to be static for a finite time period. an orange exists because you hold it and you can see it for one second, two seconds. One believes an orange exists that they see in someone else's car while passing, and the orange that was seen in a television is believed to have existed. In quantum superposition (I'm not that informed on it) a photon or electron appears to a human as existing twice, or more than twice, hence not existing at all. This idea of something 'being' in multiple locations in space during one finite moment of time, humans conclude that this object is transcendent. But maybe, these things do exist. Using the definition of existence as being 'static' for a finite period of time, and stretching this to our knowledge of infinity as being non-experiencable or understandable, we can reconcile these photons and electrons. we may say that this photon does indeed exist, and is static in one place for an immeasurable amount of time, 'infinitely' small. In the same way that once you manipulate an infinite set, thereby treating it as an infinitely large finite set, you 'ruin' things that are so small. For example, the 'observer effect', seems to affect the state of the observed through the act of observation, because by observing a set (as humans observe things and process them within perceptibly finite amounts of time), one is destroying the 'sanctity' of this infinite 'entity' or existence. Some things can only exist by not existing.

Guys, I'm going to start counting 'countable infinity', and won't stop until this project is finished…wish me luck

Nami will be so mad looking at the second demonstration (the money one)

9:58 aba mentioned

I kinda understood everything in this but I don't understand why that… matters?