## 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.…