As an informatician, I have to deal with maths a lot.
But recently, I got to an interesting problem:
If 0.999... == 1, then why can't we extend this to 0.999...8, and then go down, until 1 == 0 and therefor 1 == 2?
Going down like this is in fact is possible. (I'm basing myself on https://en.wikipedia.org/wiki/Aleph_number)
If you were to go down like this, 1 would equal 2, and 1 would also equal to 100 and so on.
This is in fact very strange, until we think about quantum physics: There, Tiles can have many different states.
As no one knows, whether maths are created by humans or not, We could change this rule, by simply proving it to be true. Based on quantum physics, https://en.wikipedia.org/wiki/Quantum_mechanics. This would also prove the Quantum theory to be true on a much bigger Scale. Imagine your Home going away, when no one Looks at it.
BUT: If we want to prove, that 1 == 2, we need to prove, that we can entirely calculate down the numbers after the period. INFINITELY LONG.
For this, we need to prove, that Infinity - Infinity = 0.
Normally, this doesn't apply, but as said: no one is sure, whether maths are natural, or created by the human.
Normally to prove this wrong, the mind-experience of pythagoras and his tortoise is stated, BUT the human has an unfair chance: He is much faster and can do much bigger steps. Infinity however goes up at the same speed, as it is just stupid counting upwards to infinity.
1 - 1 = 0
2 - 2 = 0
3 - 3 = 0
4 - 4 = 0
5 - 5 = 0
and so on.
I know, I'm bending alot of the rules of maths, but this was just a little theory I wondered about. Tell me your thougts about it in the comment-section ;-)