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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 positive if it is greater than zero, and negative if it is less than zero. Zero is defined as neither negative nor positive. The ordering of integers is compatible with the algebraic operations in the following way: If a < b and c < d, then a + c < b + d; If a < b and 0 < c, then ac < bc
the product of a negative number—al-nāqiṣ (loss)—by a positive number—al-zāʾid (gain)—is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative ...
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: A number is strictly positive if it is greater ...
A positive integer with more divisors than any smaller positive integer. A002182: Superior highly composite numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A positive integer n for which there is an e > 0 such that d(n) / n e ≥ d(k) / k e for all k > 1. A002201: Pronic numbers: 0, 2, 6, 12, 20, 30, 42, 56, 72 ...
For example, the sequence (with ordinality) of all positive odd integers followed by all positive even integers {,,,,,;,,,,,} is an ordering of the set (with cardinality ) of positive integers. If the axiom of countable choice (a weaker version of the axiom of choice ) holds, then ℵ 0 {\displaystyle \aleph _{0}} is smaller than any other ...
If the variable has a signed integer type, a program may make the assumption that a variable always contains a positive value. An integer overflow can cause the value to wrap and become negative, which violates the program's assumption and may lead to unexpected behavior (for example, 8-bit integer addition of 127 + 1 results in −128, a two's ...
a highly abundant number has a sum of positive divisors that is greater than any lesser number; that is, σ(n) > σ(m) for every positive integer m < n. Counterintuitively, the first seven highly abundant numbers are not abundant numbers. a prime number has only 1 and itself as divisors; that is, d(n) = 2