Negative Numbers

Negative numbers were not needed initially for counting or measuring, but came up mathematically as soon as subtraction was used as a process. Subtracting a larger number from a smaller number yields a negative number. A negative number is any real number less than zero. Thought as useless by most ancient cultures, one of the earliest evidences of negative numbers is from 7th century India for accounting debt. The usefulness of negative numbers was argued in mathematics into the renaissance in the 17th century. The inclusion of zero and the whole negative numbers with the natural numbers completes the set of all integers. There is a restriction in power functions that involves negative numbers because a square root can not be taken of a negative number. When multiplying any number by itself an even number of time the result is always a positive number. A positive number is defined as any real number greater than zero. A positive number times a positive number or a negative number times a negative number will always yield a positive result. A positive number times a negative number is always a negative number. The absolute value of a negative number is the positive of the same number.

The negative numbers include the negative integers -1, -2, -3, -4, -5 . . .