Re^3: What is zero divided by zero anyway?

[Aristotle]

Yes, and it gets weirder than that if you think further along those lines. In sets beyond the natural numbers, among the real numbers f.ex, any two numbers are separated by an infinite set of numbers. In fact, because you can translate any set of reals delimited by two numbers (exclusive) to any other set of reals delimited by any two numbers (exclusive) with a single multiplication, this means that the distance between any two numbers is equally large.

F.ex, the set of numbers between 1.0 and 2.0 exclusive is inifinite. No matter how many members you assume, there are still more numbers between those. The same is true for the set of numbers between 2.0 and 10.0 - it is infinite. But although the interval from 1.0 to 2.0 exclusive is of length 1, and that from 2.0 to 10.0 exclusive is of length 8, you can map the set { x ∈ R ; 1.0 < x < 2.0 } to set { x ∈ R ; 2.0 < x < 10.0 } by simply multiplying by 8.

As I said on the onset of this thread: zero and infinity are deep voodoo. Zero is deceptively so, it looks innocent at first, but it's still voodoo.

Makeshifts last the longest.