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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. [11] 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). [12]
Positive numbers: Real numbers that are greater than zero. 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 ...
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.
In mathematics real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra. The word is also used as a noun, meaning a real number (as in "the set of all reals").
Magnitudes are always non-negative real numbers, and to any non-zero number there belongs a positive real number, its absolute value. For example, the absolute value of −3 and the absolute value of 3 are both equal to 3. This is written in symbols as | −3 | = 3 and | 3 | = 3.
This allows one to easily determine inverses of many functions that are given by algebraic formulas. For example, if f is the function = (+) then to determine () for a real number y, one must find the unique real number x such that (2x + 8) 3 = y. This equation can be solved:
In fact, the rules for additive and multiplicative inverses are both examples of applying a strictly monotonically decreasing function. A few examples of this rule are: Raising both sides of an inequality to a power n > 0 (equiv., −n < 0), when a and b are positive real numbers:
Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. ... Floor function: if x is a real number, ...