Wacky infinites headache

[Peegee]

..well not really if you understand it, but some people might get their brains to explode. I'm trying to do this here.

There's two ways to do this: the numbers way and the square way

Numbers way:

I will first prove that there are infinite real numbers between any two integers.

for any real number x between 0 and 1 (say, 0.5 or 0.25) you have another number x/2 or x/y where y is a real number. Doesn't matter. You can do this for any of them. Since you can progressively divide x / y^whatever, there's always another number.

I'll assume you understand. Moving on.

We now have established infinite numbers between 0 and 1. What about 1 and 2? 1 and 2 also has infinite numbers between them. The set is the same as the first set, with each number increased by 1.

But wait, we now have two sets of infinite numbers.

I now ask you. How many numbers between 0 and 2? The answer: infinity.

So we have infinite numbers between 0 and 1 and infinite numbers between 1 and 2 and infinite numbers between 0 and 2.

confusing the average person time: OMG THERE'S THE SAME AMOUNT NUMBERS BETWEEN 0 AND 2 AND 0 AND 1 AND 1 AND 2, EVEN THOUGH I CAN COUNT TWICE THE AMOUNT OF NUMBERS BETWEEN 0 AND 2 AND 0 AND 1 BY TRACING EACH NUMBER TO ITS CORRESPONDING POINT BETWEEN 1 AND 2 LOLOLOLOLOLOLOL

SQUARE METHOD

I have to do this fast cuz I posted too quick.

- infinite points in a line, right? (see number portion for proof)
- infinite points in 2nd line, right?
- how many points in a square?
- infinity? more than infinity? wtf?

solution to problem = where?



Actually don't answer that just yet. Maybe some people will post and go 'wtf my brain hurts'.