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In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division). [2]
Some real numbers have decimal expansions that eventually get into loops, endlessly repeating a sequence of one or more digits: 1 ⁄ 3 = 0.33333... 1 ⁄ 7 = 0.142857142857... 1318 ⁄ 185 = 7.1243243243... Every time this happens the number is still a rational number (i.e. can alternatively be represented as a ratio of an integer and a ...
Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.
For example, in the Python programming language, int represents an arbitrary-precision integer which has the traditional numeric operations such as addition, subtraction, and multiplication. However, in the Java programming language , the type int represents the set of 32-bit integers ranging in value from −2,147,483,648 to 2,147,483,647 ...
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.
The width, precision, or bitness [3] of an integral type is the number of bits in its representation. An integral type with n bits can encode 2 n numbers; for example an unsigned type typically represents the non-negative values 0 through 2 n − 1.
In Python, the int type has a bit_count() method to count the number of bits set. This functionality was introduced in Python 3.10, released in October 2021. [17] In Common Lisp, the function logcount, given a non-negative integer, returns the number of 1 bits. (For negative integers it returns the number of 0 bits in 2's complement notation.)
In computer science, a literal is a textual representation (notation) of a value as it is written in source code. [1] [2] Almost all programming languages have notations for atomic values such as integers, floating-point numbers, and strings, and usually for Booleans and characters; some also have notations for elements of enumerated types and compound values such as arrays, records, and objects.