# 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)

• 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 .

• Infinitive

[in-fin-i-tiv] /ɪnˈfɪn ɪ tɪv/ Grammar noun 1. a verb form found in many languages that functions as a noun or is used with auxiliary verbs, and that names the action or state without specifying the subject, as French venir “to come,” Latin esse “to be,” fuisse “to have been.”. 2. (in English) the simple or […]

Disclaimer: Infinite set definition / meaning should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional. All content on this website is for informational purposes only.