# Thread: Infinite within the infinite? Parallel universes.

1. Hello everyone,

I suppose you all know the "parallel universe" theory, which states that for every thing we do (ex. take a step), there are the other infinite things we didn't do instead (ex. say yippie-kay-yeah and jump 3 times), but on a different parallel universe, we did that thing that we didn't do in this one. This goes on to a infinite number of parallel universes, where a molecular change could be the only thing that made that parallel universe different to another one.

So I was thinking of how at least I have a girlfriend in another parallel universe, when I suddenly realised the sun. You see, the sun is a star (duh), and it is burning hot, lets say to a 5527°C on the surface. OK I thought, cool. But on another parallel universe it is probably at 5528°C. Ah nice, I thought. But then I realised that I didn't take into account the coma "," (dot in america). Oh, so the sun might be in a parallel universe at 5528,20000008°C and on another one at 5528.200000081°C. OH, and the pattern goes to an infinite number after the coma (dot in america). So since numbers are infinite, there must be an infinite number of parallel universes for the infinite numbers there are on maths.

So is that possible? Infinite within the infinite? And just how big is the infinite number of parallel universes? certainly bigger than the infinite numbers there are in maths, since it must cover those up, and all the other stuff there is too (taking a step or not).

To clarify the idea, I remember this "size of infinite" theory, that says that although numbers are infinite, the "infinite number" of prime numbers (2, 3, 5, 7, 11, etc.) is smaller than the "infinite number" of natural numbers (1,2,3,4,5,6,etc.).

SO THE REAL QUESTION:
Is that possible, infinite within the infinite? and does that "size of infinite" theory apply to the parallel universes, so that the "infinite number" of parallel universes is bigger than the "infinite number" of normal math numbers?  2.

3. Personally, I don't think that anything can be infinite.  4. Personally, I don't think that anything can be infinite.
All right. Count all the natural numbers. When you reach the very last number, let me know. I'll be the first to accept that the set of all natural numbers is finite.

Even better, tell me the number of points within a single, finite line, and I'll believe you.  5. Originally Posted by Liongold
All right. Count all the natural numbers. When you reach the very last number, let me know. I'll be the first to accept that the set of all natural numbers is finite.
Numbers are a human invention. The largest number is the largest number that a human has ever conceived, and I don't know what number that is.
What is the largest number you can think of? Write the number 9 over and over and over and you will get a very large number, but it won't be infinite. You might be clever and write the number as an exponent (ie 9 to the power of 9 to the power of 9) but its still not infinite.
Even better, tell me the number of points within a single, finite line, and I'll believe you.
There is a smallest unit of length. I don't know what it is but for the sake of argument, let's call it the "Planck length". The number of points would then be the length of the line divided by the "Planck length".  6. There is a smallest unit of length. I don't know what it is but for the sake of argument, let's call it the "Planck length". The number of points would then be the length of the line divided by the "Planck length".
I'm assuming here on that you mean the actual Planck length, common to physics. In that case, let me remind you that the Planck length can, in itself, be defined as a line of certain length equal to the Planck length.

Therefore, since the Planck length multiplied by the number of points is equal to the length of the line, this implies that the Planck length is equal to the size of a point.

Therefore, this implies that a point is a line.

Admittedly, geometry has never attempted to really define a point or a line - Euclid's definitions are themselves self-contradictory - but there exists a clear distinction between the two, as should be readily obvious. By assuming the notion of the smallest length, you have directly proved that points are equivalent to lines, which is impossible.

I shouldn't really criticise this, however, since I happen to be working on the notion that a smallest unit does exist.It does have the singular advantage, though, of being able to show that the operation of division by this number always results in inifinity, which tends to nullify your point again. However, this is not the place to talk about my ideas, so please ignore this.

How do you respond?

Numbers are a human invention.
Not necessarily. The concept of a number is a human invention; the thing to which it refers to need not necessarily refer to. For example, the fact that two oranges are greater than one is not in itself a human invention - the way we think about this, by referring to the notion of an orange, labelling the property by which we differentiate between the two a 'number', though, is decidedly human, however.

But let us move on.

The largest number is the largest number that a human has ever conceived, and I don't know what number that is.
That is a strange position to take. One can show readily that the largest possible number does not exist, merely by your definition.

Let us assume your definition holds true. Let us term the largest possible number ever imagined as . However, adding 1 to should yield a larger number.

Therefore, where Xb refers to the previous largest possible number ever imagined and Xa the new number.

However, again adding one to Xa yields a greater number, and adding one to it yields an even greater one, and so on. Since the axioms of arithmetic hold that the operation of addition is possible for all numbers, it is possible to add one on and on and on, each time rendering the a greater and greater number. Since this process cannot stop until the axioms of arithmetic no longer hold, which is impossible, it should be clear that there exists an infinite number of numbers.

Care to argue?  7. You guys are way off topic.

To OP:

The "theory" that you're mentioning, I've never heard of. However, if that is all it states, then it has nothing to do with what you're asking.

The reason the set of prime numbers is smaller than the set of infinite numbers is because of the definition of a prime number.

Step by step:
1. Let there be 2 number lines, N1 and N2.
2. Let them both end at Inf.
3. For N1: Let there be a "tick mark" at every number in the set of real numbers.
4. For N2: Let there be a "tick mark" at every number in the set of real prime numbers.
5. For demonstration purposes, on each line, tick off an integer that fits the criteria of the line. For N1, put a tick mark at every number between 1 and 100. For N2, put a tick mark at every number between 1 and 100 that is prime.
6. Notice how, because not every number is prime, there are less tick marks on N2.

Though both sets will be "infinite," if you stop counting at any point and tally the numbers on both lines, you will inevitably find that there are less on N2 than N1. However, there are still an infinite number of both as we do not have a maximum value we can count to. It is only when we impose a maximum number, and stop the counting process, that we find this theory to be true.

That being said, there is no reason you cannot have an infinite set within an infinite set, if both sets are not defined exactly equal. We just showed this with the set of primes inside of the set of reals, since both are infinite sets when allowed to grow infinitely.  8. Originally Posted by Liongold
Care to argue?
I'd love to. I think this discussion is very interesting, and I like to keep it going. Sounds like we are off topic though, so I am going to start a new thread in this forum.  Bookmarks
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