infinite

infinite (ˈɪnfɪnɪt)
—adj
1.	a.  having no limits or boundaries in time, space, extent, or magnitude
	b.  (as noun; preceded by the): the infinite
2.	extremely or immeasurably great or numerous: infinite wealth
3.	all-embracing, absolute, or total: God's infinite wisdom
4.	maths
	a.  having an unlimited number of digits, factors, terms, members, etc: an infinite series
	b.  (of a set) able to be put in a one-to-one correspondence with part of itself
	c.  Compare finite (of an integral) having infinity as one or both limits of integration
'infinitely
—adv
'infiniteness
—n

infinite

infinite   (ĭn'fə-nĭt)  Pronunciation Key  Relating to a set that can be put into a one-to-one correspondence with some proper subset of its own members. Relating to or being a numerical quantity describing the size of such a set. Being without an upper or lower numerical bound.

infinite

adj. [common] Consisting of a large number of objects; extreme. Used very loosely as in: "This program produces infinite garbage." "He is an infinite loser." The word most likely to follow `infinite', though, is hair. (It has been pointed out that fractals are an excellent example of infinite hair.) These uses are abuses of the word's mathematical meaning. The term `semi-infinite', denoting an immoderately large amount of some resource, is also heard. "This compiler is taking a semi-infinite amount of time to optimize my program." See also semi.

infinite definition

mathematics
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.
[Jargon File]
(1995-03-29)