Proof by Contradiction

The concept of proof by contradiction refers to taking a statement and assuming the opposite is true. When assuming the opposite is true we begin to further examine the our ‘opposite’ statement and reach to a conclusion which doesn’t add up or in simple terms is absurd.

Take the case:

Statement: There are infinite number of prime numbers.

Using the concept of proof by contradiction, we will assume the opposite is true.

If an integer (2) divides an integer (6) we say that 2 divides 6 or 2|6. In a more general sense we can say that if any integer ‘a’ divides any other integer ‘b’ then a|b.

Prime numbers: it is an integer (n ≥ 2) that has exactly two positive factors (1 and itself).

eg. 2, 3, 5 …

Composite numbers: it is an integer (n ≥ 2) that has more than two positive factors.

eg. 4, 6, 8 …

Fundamental Theorem of Arithmetic: Every integer n ≥ 2 has a unique (exactly one) prime factorization.…