For a more detailed and technical article, see Ramsey's theorem.

For other similarly named results, see Birkhoff's theorem (disambiguation).

The group acts on itself by the left multiplication (see Cayley's theorem).

Sometimes a loss of precision is necessary to make the semantics decidable (see Rice's theorem, halting problem).

However, a measurable function is nearly a continuous function; see Luzin's theorem.

For a more complete account of this proof, see Cantor's theorem.

Due to the limited bandwidth, information can only be transmitted very slowly, on the order of a few characters per minute (see Shannon's coding theorem).

For more on this topic, see Haag's theorem.

See Budan's theorem for a description of the historical background of these methods.

Furthermore, the eight digits have complementary halves (see Midy's theorem).