Proofs

An axiom of a mathematical system is a statement that is assumed to be true. No proof is given. From axioms we derive propositions and theorems.

With a "symmetric" statement (e.g and is odd), it is only necessary to prove one case and to write "without loss of generality" (e.g without loss of generality, prove for is odd and is even...)

An integer is even if it can be written as for , and is odd for for

Symbols listed from highest to lowest precedence: