Math

[JaeSon15]

Actually, the set of numbers between 1 and 2 has the same size as those between 1 and 3. The proposition which was crazy back then, though fairly accepted today, was that a line segment can be put into correspondence with a square.

So really when you're dealing with infinite sets, there are only two sizes: countably infinite and uncountably infinite.

So, here's another counterintuitive example: The set of natural numbers has cardinality equal to the set of integers. This almost doesn't make sense, but here's one particular correspondence: (1,0), (2, -1), (3, 1), (4, -2), (5, 2), (6,-3), (7, 3), ...