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For example, −3 represents a negative quantity with a magnitude of three, and is pronounced and read as "minus three" or "negative three". Conversely, a number that is greater than zero is called positive; zero is usually (but not always) thought of as neither positive nor negative. [2]
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. Non-positive numbers: Real numbers that are less than or equal to zero. Thus a non-positive number is either zero or negative.
The plus and minus symbols are used to show the sign of a number. In mathematics, the sign of a real number is its property of being either positive, negative, or 0.Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign.
The same convention is also used in some computer languages. For example, subtracting −5 from 3 might be read as "positive three take away negative 5", and be shown as 3 − − 5 becomes 3 + 5 = 8, which can be read as: + 3 −1(− 5) or even as + 3 − − 5 becomes + 3 + + 5 = + 8.
An integer is the number zero , a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]
As a consequence, a product of two negative numbers is positive. For an algebraic proof of this result, start with the equation 0 = −1 ⋅ 0 = −1 ⋅ [1 + (−1)]. The first equality follows from the above result, and the second follows from the definition of −1 as additive inverse of 1: it is precisely that number which when added to 1 ...
In elementary mathematics, the additive inverse is often referred to as the opposite number, [3] [4] or its negative. [5] The unary operation of arithmetic negation [ 6 ] is closely related to subtraction [ 7 ] and is important in solving algebraic equations . [ 8 ]
My example of {0,1,2,3} above would work well (with addition modulo 4). It's still true that 1<2 without a negative number in sight. Certes 15:44, 3 May 2021 (UTC) And 2 < 1 since 2+3 = 1. As for "negative" numbers, the concept isn't useful in this case since every element can be regarded as both positive and negative.