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In a sense, subtraction is the inverse of addition. That is, c = a − b if and only if c + b = a. In words: the difference of two numbers is the number that gives the first one when added to the second one. Subtraction follows several important patterns. It is anticommutative, meaning that
If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (martaba khāliyya), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number. [5]
Several algorithms in number theory and cryptography use differences of squares to find factors of integers and detect composite numbers. A simple example is the Fermat factorization method , which considers the sequence of numbers x i := a i 2 − N {\displaystyle x_{i}:=a_{i}^{2}-N} , for a i := ⌈ N ⌉ + i {\displaystyle a_{i}:=\left\lceil ...
The integers arranged on a number line. 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]
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Fractions are written as two integers, the numerator and the denominator, with a dividing bar between them. The fraction m / n represents m parts of a whole divided into n equal parts. Two different fractions may correspond to the same rational number; for example 1 / 2 and 2 / 4 are equal, that is:
For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a collection of operations if it is closed under each of the operations individually.
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping ...