# Infinity

Cantor showed that infinities come in different sizes. The counting numbers can be listed one after another, and the real numbers cannot. His diagonal argument builds a number that differs from the n-th entry of any list in its n-th digit. A close cousin of that move sits inside Gödel’s proof.

Connects to:
- [Math](https://mapideas.org/i/math)
- [Gödel](https://mapideas.org/i/godel)
- [closed loops](https://mapideas.org/i/tr_loops)
- [Zero](https://mapideas.org/i/mat_zero)
- [Where do numbers live?](https://mapideas.org/i/q_math_exist)
- [Is there a size between?](https://mapideas.org/i/q_math_between)
- [Which new axioms should we add?](https://mapideas.org/i/q_g_axioms)

Sources:
- [Wikipedia: Cantor’s diagonal argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)
- [Wikipedia: Georg Cantor](https://en.wikipedia.org/wiki/Georg_Cantor)

Source: https://mapideas.org/i/mat_infinity · open on the map: https://mapideas.org/#mat_infinity