Algebraic Equivalence and Proof

Algebraic equivalence are rules applied in Maths to show that when two things are added or multiplied together, usually the relationship between even and odd numbers, a specific outcome is given.

Rules of odd and even numbers

The following rules apply for any even or odd numbers:

even+even=eveneven\times even=even
odd+odd=evenodd\times odd=odd
even+odd=oddeven\times odd=even
odd+even=oddodd\times seven=even

We prove all of these in a similar way.

To represent an even number, it is indicated as 2x, where x is any natural number. To represent an odd number, it is indicated as 2x+1, where x is any natural number.

To prove even+even=even, we take two even numbers, namely 2a and 2b, where a and b are natural numbers.


As we can factor a two out of the sum of 2a and 2b, it shows that it is also even and therefore it has been proven.

Key fact: proofs are not proofs if you try and use an example to prove a concept!