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a. having an unlimited number of digits, factors, terms, members, etc.
b. (of a set) able to be put in a one-to-one correspondence with part of itself
c. (of an integral) having infinity as one or both limits of integration


Larger than any fixed number.


1. Bigger than any natural number. There are various formal set definitions in set theory: a set X is infinite if

(i) There is a bijection between X and a proper subset of X.

(ii) There is an injection from the set N of natural numbers to X.

(iii) There is an injection from each natural number n to X.

These definitions are not necessarily equivalent unless we accept the Axiom of Choice.

2. The length of a line extended indefinitely.

See also infinite loop, infinite set.
References in periodicals archive ?
Joseph Brodsky speaks of the pain of exile, "but also the pain-dulling infiniteness, forgetfulness, detachment, indifference" (Robinson, 1994:269 and 11).
If, then, Guillevic's sense of a "love / That will engulf you / In the infiniteness / Of what calls out to us" continues to maintain itself, if that "Something / That bears you up, / .
From this series of processes, in the exchange between the body and the material, a shape is born, always unique and always brought into question--the inventory on display only pointing up the infiniteness of the shapes' possible variations.
The infiniteness and restlessness of man's actions and desires, not his finitude or possible saturation, is Hayek's leading societal image.