# Is there a size between?

**Is there an infinity between the counting numbers and the real numbers?**

This is the continuum hypothesis. Gödel showed in 1940 that the usual axioms cannot disprove it, and Cohen showed in 1963 that they cannot prove it. Whether it has an answer at all is still argued.

Connects to:
- [Infinity](https://mapideas.org/i/mat_infinity)
- [Gödel](https://mapideas.org/i/godel)

Sources:
- [Wikipedia: Continuum hypothesis](https://en.wikipedia.org/wiki/Continuum_hypothesis)

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