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In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [9] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11).
In mathematics, a negative number is the opposite (mathematics) 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.
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.
Some elementary teachers use raised minus signs before numbers to disambiguate them from the operation of subtraction. [21] 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:
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
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]
This is a point often badly taught in grade school and still misunderstood by some college students. A negative number represents the opposite of a positive number. If, for example, +10 represents a ten dollar profit, then -10 represents a ten dollar loss. The reciprocal is not an opposite. 1/10 does not represent the opposite of a profit.
Since a real number and its opposite have the same absolute value, it is an even function, and is hence not invertible. The real absolute value function is a piecewise linear, convex function. For both real and complex numbers the absolute value function is idempotent (meaning that the absolute value of any absolute value is itself).