The math proofs that will be covered in this website fall under the category of basic or introductory proofs. They are considered “basic” because students should be able to understand what the proof is trying to convey, and be able to follow the simple algebraic manipulations or steps involved in the proof itself. The pre-requisite subject of these lessons is Algebra 1.

[latex]\sqrt 2[/latex] is irrational

If [latex]a < b[/latex], then [latex]a < {\Large{{{a + b} \over 2}}} < b[/latex]

If [latex]a|b[/latex] and [latex]b|c[/latex], then [latex]a|c[/latex]

If [latex]n^2[/latex] is even, then [latex]n[/latex] is even

If [latex]n^2[/latex] is odd, then [latex]n[/latex] is odd

Mathematical Induction (Divisibility)

Mathematical Induction (Summation)

Proof by Contradiction

Square Root of a Prime Number is Irrational

Sum of Two Even Numbers is an Even Number

Sum of Two Odd Numbers is an Even Number

There are infinitely many prime numbers