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The Collaborative International Dictionary

Divisibility \Di*vis`i*bil"i*ty\, n. [Cf. F. divisibilit['e].] The quality of being divisible; the property of bodies by which their parts are capable of separation.

Divisibility . . . is a primary attribute of matter.
--Sir W. Hamilton.


n. 1 (context uncountable English) The state of being divisible. The state capable of being divided. 2 (context arithmetic English) The property of being divisible by a particular integer.


n. the quality of being divisible; the capacity to be divided into parts or divided among a number of persons

Divisibility (ring theory)

In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. See the article on divisors for this simplest example. With the development of abstract rings, of which the integers are the archetype, the original notion of divisor found a natural extension.

Divisibility is a useful concept for the analysis of the structure of commutative rings because of its relationship with the ideal structure of such rings.

Usage examples of "divisibility".

The divisibility of this is founded on the divisibility of space, which constitutes the possibility of the body, as an extended whole.

For the infinity of the division of a given phenomenon in space is founded simply on this, that by it divisibility only, that is, an entirely indefinite number of parts, is given, while the parts themselves can only be given and determined through the subdivision, in short, that the whole is not itself already divided.

No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinitive divisibility of extension, with its consequences.

Leibniz similarly insists on the infinite divisibility of matter, with differences animating it on every scale.

The fact of the vast diffusion of some odors, as that of musk or the rose, for instance, has long been cited as the most remarkable illustration of the divisibility of matter, and the nicety of the senses.

To MORE this seemed like denying the existence of spirit, which he regarded as extended, and he postulated divisibility and impenetrability as the chief characteristics of matter.