Prove that the product of two odd numbers is always odd.

Odd Number (1): 2n₁+1

Odd Number (2): 2n₂+1



(2n₁+1)(2n₂+1)

= 4n₁n₂ + 2n₁ + 2n₂ + 1

= 2(2n₁n₂ + n₁ + n₂) + 1

Call (2n₁n₂ + n₁ + n₂) a number... Therefore...

= 2n+1 (which must be odd as odd numbers are represented as thus)

*Note that a natural number multiplied by a natural number always produces a whole or natural number. (n) stands for a natural number and furthermore, a natural number added to a natural number produces a natural number. Odd numbers are represented using the expression 2n+1.