Full Idea
Cantor's Theorem (1874) says there are infinite sets that are not enumerable. This is proved by his 1891 'diagonal argument'.
Gist of Idea
There are infinite sets that are not enumerable
Source
report of George Cantor (works [1880]) by Peter Smith - Intro to Gödel's Theorems 2.3
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.14
A Reaction
[Smith summarises the diagonal argument]