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Integer. The set of integers on a number line. An integer is the number zero ( 0 ), 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]
A probable example is Fermat's Last Theorem. The definition of the integers as sets satisfying Peano axioms provide a model of Peano arithmetic inside set theory. An important consequence is that, if set theory is consistent (as it is usually guessed), then Peano arithmetic is consistent. In other words, if a contradiction could be proved in ...
Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]
Negative number. This thermometer is indicating a negative Fahrenheit temperature (−4 °F). In mathematics, a negative number represents an opposite. [ 1] In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency.
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 to zero. Thus a non-negative number is either zero or positive.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [ 1][ 2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a ...
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. [ 1][ 2] The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two.
In number theory, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is called a composite number, or it is not, in which case it is called a prime number.