A proof is a strict logical argument that demonstrates with mathematical certainty that a statement is true.

For SL students, these proofs will be in the form

Prove that

where ≡ means equivalent, i.e. equal for ALL variables in the expression, not just some specific intersections.

We use LHS (left-hand side) and RHS (right-hand side) as an abbreviation for one side of the equivalence.

The parity of an integer describes whether or not it is divisible by 2. We say that

In general, even numbers take the form n=2k, and odd numbers take the form n=2k+1 for some k∈Z.