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In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.
Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive.
A number is negative if it is less than zero. A number is non-negative if it is greater than or equal to zero. A number is non-positive if it is less than or equal to zero. When 0 is said to be both positive and negative, [citation needed] modified phrases are used to refer to the sign of a number: A number is strictly positive if it is greater ...
Negative numbers are usually written with a negative sign (a minus sign). As an example, the negative of 7 is written −7, and 7 + (−7) = 0. When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, Z also written .
When it is placed immediately before an unsigned number, the combination names a negative number, the additive inverse of the positive number that the numeral would otherwise name. In this usage, '−5' names a number the same way 'semicircle' names a geometric figure, with the caveat that 'semi' does not have a separate use as a function name.
In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element. In elementary mathematics, the additive inverse is often referred to as the opposite number. [3] [4] The concept is closely related to subtraction [5] and is important in solving algebraic equations. [6]
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The whole numbers were synonymous with the integers up until the early 1950s. [23] [24] [25] In the late 1950s, as part of the New Math movement, [26] American elementary school teachers began teaching that whole numbers referred to the natural numbers, excluding negative numbers, while integer included the negative numbers.