OOTS #1277 - The Discussion Thread

[HalfTangible]

Logically this appears to be true.

It is not.

Infinity is not logical to minds that have trouble counting past 20. But the entire infinity of numbers, (a bounded infinity because it excludes everything except numbers,) can be divided exactly the same number of times as the infinity between 2 and 3.

Infinity = infinity

There are infinite natural numbers (1, 2, 3, 4, 5, 6...) but there's also an infinite series of real numbers in between each of those natural numbers. The infinite real numbers include all of the infinite natural numbers, because natural numbers are also real numbers. So the infinite number of real numbers is larger than the infinite number of natural numbers.

Not all infinities are equal.