MagicBell wrote:The proof that there are more values between, say, 1 and 2, than there are integers (whole numbers).
MB, This is one is quite easy. For any positive integer that you care to think of, there is an equivalent item in the 0-1 range, namely its reciprocal (n -> 1/n). So there are at least as many items on the range 0-1 as there are positive integers.
Where it starts getting spooky is that the same logic applies to
any positive numbers, whether integers or not. On this one-to-one basis, it is correct that there are as many 'numbers' between 0 and 1 as there are between 0 and as high as you want to go, because for any one you pick in either set, you can find the other in the other set as its reciprocal.
Super spookiness comes when you find out that this infinity number (usually known as aleph null) is not the end of the game. There are other sets of countable things which cannot be counted using this 'basic' infinity.
As you say, we have moved far from a Magic forum.