Intelligent Infinity Defined

[Anders]

It's extremely sneaky how infinite sets are used in math. Take for example A = {0, 1, 2, 3, ...} and B = {-1, -2, -3, -4, ...} and then when combining those two supposedly completed infinite sets with a union it results in the set of integers Z. So what's wrong with that? The problem as I see it is that A expands in one direction, B expands in one direction, while Z expands in two directions! Apples and oranges.

So even adding infinite sets with ordinary union is invalid as I see it. It's possible to write Z as {0, 1, -1, 2, -2, 3, -3, ...} but that just hides the fact that it's an expansion in two directions.