Well, it didn't disprove infinity, but it did demonstrate that you have to be careful when thinking about in infinity. Infinity is not a number. You cannot ever "reach" infinity.Ibn Taymiyyah wrote: 5) Therefore they will never become infinite in size because they will never become equal (point (1)).
Deep inside I know that there is something wrong with this argument but I can’t put my finger on it.
For any number x you can imagine x+1. So you cannot imagine a number x such that x=infinity. There is no such number. But you can imagine incrementing x forever, so that x increases towards infinity.
If an object is "infinite in size," it means that we can't evaluate its size. Whatever number x we propose as being the size, there is always another number x+1, larger than the one we propose. Ordinarily, we cannot say that two objects of "infinite size" are equal in size, because we have no sizes to compare.Ibn Taymiyyah wrote: 1) We cannot imagine two objects that are infinite in size to be anything but equal in size.
But check out the link annis posted about Georg Cantor and transfinite numbers.
Here is one of Canor's observations: Imagine the set N of all natural numbers (1,2,3,4,5,6.....). Now eliminate all the even numbers, so we are left with set O=(1,3,5,7,9...). Common sense tells you that set O is half as big as set N, right? But both O and N are still "infinite in size," even though we removed every other item from set N to get set O. In fact, for every item in N, we can find another item in O to pair it with, as if they were equal in size. Weird, huh?