Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts. Examples of odd numbers are 3, 5, 7, 9, 11, 13, 15, & Examples of even numbers are 2, 4, 6, 8, 10, 12, 14, &

If n is odd then by definition we can write n = 2m + 1 for some integer m. Then n +1= 2m+2 = 2(m+1). Note that m+1 is the sum of two integers, hence is an integer.