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If n is a negative integer, is defined only if x has a multiplicative inverse. [35] In this case, the inverse of x is denoted x −1, and x n is defined as (). Exponentiation with integer exponents obeys the following laws, for x and y in the algebraic structure, and m and n integers:
He may have been the first mathematician to recognize zero and negative numbers as exponents. [ 1 ] In 1475, Jehan Adam recorded the words "bymillion" and "trimillion" (for 10 12 and 10 18 ) and it is believed that these words or similar ones were in general use at that time.
Signed zero is zero with an associated sign.In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in ...
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
A number is positive if it is greater than zero. 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:
Two to the power of n, written as 2 n, is the number of in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to an an 'unsigned integer', can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent. That is, = (). Together, these may be implemented directly as the following recursive algorithm:
The concept of negative numbers itself is significantly older and was first explored in Chinese mathematics in the first millennium BCE. [172] Indian mathematicians also developed the positional decimal system used today, in particular the concept of a zero digit instead of empty or missing positions. [173]
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