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# Infinite set

mathematics
A set with an infinite number of elements. There are several possible definitions, e.g.
(i) (“Dedekind infinite”) A set X is infinite if there exists a bijection (one-to-one mapping) between X and some proper subset of X.
(ii) A set X is infinite if there exists an injection from N (the set of natural numbers) to X.
In the presence of the Axiom of Choice all such definitions are equivalent.
(1995-03-27)

Tagged:

• Infinitesimal

[in-fin-i-tes-uh-muh l] /ˌɪn fɪn ɪˈtɛs ə məl/ adjective 1. indefinitely or exceedingly small; minute: infinitesimal vessels in the circulatory system. 2. immeasurably small; less than an assignable quantity: to an infinitesimal degree. 3. of, relating to, or involving infinitesimals. noun 4. an infinitesimal quantity. 5. Mathematics. a variable having zero as a limit. /ˌɪnfɪnɪˈtɛsɪməl/ adjective […]

• Infinitesimal-calculus

noun 1. the differential calculus and the integral calculus, considered together. noun 1. another name for calculus (sense 1)

• Infinitesimally

[in-fin-i-tes-uh-muh l] /ˌɪn fɪn ɪˈtɛs ə məl/ adjective 1. indefinitely or exceedingly small; minute: infinitesimal vessels in the circulatory system. 2. immeasurably small; less than an assignable quantity: to an infinitesimal degree. 3. of, relating to, or involving infinitesimals. noun 4. an infinitesimal quantity. 5. Mathematics. a variable having zero as a limit. /ˌɪnfɪnɪˈtɛsɪməl/ adjective […]

• Infinitival

[in-fin-i-tahy-vuh l] /ˌɪn fɪn ɪˈtaɪ vəl/ adjective, Grammar. 1. of or relating to the .

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