nondividing

Nondividing is a term used in multiple disciplines to describe the absence of division, either in a biological or mathematical sense. It generally denotes a state or relation in which division does not occur.

In biology, nondividing cells are those that have exited the cell cycle and no longer undergo mitosis. Such cells may be quiescent (in a reversible G0 phase) or permanently post-mitotic after differentiation. Examples include most neurons and mature cardiac muscle cells. Nondividing cells typically have reduced or absent capacity to proliferate, relying instead on maintenance, repair, and, in some tissues, limited regeneration. The concept is important for understanding development, tissue maintenance, aging, and certain diseases where cell turnover is constrained.

In mathematics, nondividing describes the negation of divisibility. If a and b are integers, a does not divide b is written as a ∤ b, meaning b is not a multiple of a. For example, 3 ∤ 14, because 14 is not divisible by 3. This usage contrasts with the positive relation of divisibility, where a divides b and b equals a multiplied by some integer. Nondivisibility is fundamental in number theory, affecting properties of primes, factorization, and modular arithmetic.

The term nondividing is less commonly used as a formal technical label outside these contexts; it is typically replaced by “does not divide” in mathematics or by “post-mitotic” or “nonproliferating” in biology, depending on the domain.

See also: divisibility, post-mitotic, G0 phase, divisors, prime numbers.