Odd number

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An odd number is an integer which is not a multiple of two. If it is divided by two the result is a fraction. One is the first odd positive number. The next four bigger odd numbers are three, five, seven, and nine. Some sequential odd numbers are: {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35}.

An integer that is not an odd number is an even number. Some sequential even numbers are: {0,2,4,6,8,10,12,14,16...} If an even number is divided by two, the result is another whole number. On the other hand, an odd number, when divided by two, will result in a fraction.

Since odd and even numbers are defined only in reference to the set of integers (..., −3, −2, −1, 0, 1, 2, 3, ...), all negative numbers can also be either odd or even.

To find the set of odd natural numbers, we use 2N+1 where N is any integer.