Infinity is not a number in the usual sense, and different infinities can actually be different sizes.

The longer version

Infinity describes a size of collections, not a point on the number line, so arithmetic with it behaves oddly: adding one to an endless list leaves a list you can still match up term by term. Georg Cantor's insight was to compare infinities by pairing rather than counting, asking whether every element on one side finds a partner.

Pairing works between whole numbers and fractions, which surprises people because fractions sit densely everywhere. It fails between whole numbers and the real line: Cantor's diagonal construction builds a decimal that differs from every listed one, so no complete pairing exists. Some infinities are therefore strictly larger, and the hierarchy above continues without end.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.