Telling an equation from an identity

An equation holds for some values, an identity for all, written with ≡.

Showing two expressions are equivalent

Expanding and simplifying one side until it matches the other.

Writing even, odd and consecutive integers

Even numbers as 2n, odd as 2n + 1, consecutive integers as n and n + 1.

Higher

Proving a statement algebraically

Proving a claim for every integer at once, since examples never prove.

Higher