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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. Non-positive numbers: Real numbers that are less than or equal to zero. Thus a non-positive number is either zero or negative.
In mathematics, the natural numbers ... defining the natural numbers as the non-negative integers 0 ... each natural number has a successor and every non-zero natural ...
Non-zero or nonzero may refer to: Non-zero dispersion-shifted fiber, a type of single-mode optical fiber; Non zero one, artist collective from London, England; Non-zero-sum game, used in game theory and economic theory; Non Zero Sumness, 2002 album by Planet Funk; In mathematics, a non-zero element is any element of an algebraic structure other ...
Certain non-zero integers map to zero in certain rings. The lack of zero divisors in the integers (last property in the table) means that the commutative ring Z {\displaystyle \mathbb {Z} } is an integral domain .
Thus, the zero-product property holds for any subring of a skew field. If is a prime number, then the ring of integers modulo has the zero-product property (in fact, it is a field). The Gaussian integers are an integral domain because they are a subring of the complex numbers.
The non-negative real numbers can be noted but one often sees this set noted + {}. [25] In French mathematics, the positive real numbers and negative real numbers commonly include zero, and these sets are noted respectively + and . [26] In this understanding, the respective sets without zero are called strictly positive real numbers and ...
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function, is a member of the domain of such that () vanishes at ; that is, the function attains the value of 0 at , or equivalently, is a solution to the equation () =. [1]
An equivalent, and more succinct, definition is: a field has two commutative operations, called addition and multiplication; it is a group under addition with 0 as the additive identity; the nonzero elements form a group under multiplication with 1 as the multiplicative identity; and multiplication distributes over addition.