infinite

adj 1: having no limits or boundaries in time or space or extent or

magnitude; "the infinite ingenuity of man"; "infinite

wealth" [ant: {finite}]

2: (grammar) of verbs; having neither person nor number nor

mood (as a participle or gerund or infinitive); "infinite

verb form" [syn: {non-finite}] [ant: {finite}]

3: too numerous to be counted; "incalculable riches";

"countless hours"; "an infinite number of reasons";

"innumerable difficulties"; "the multitudinous seas";

"myriad stars"; "untold thousands" [syn: {countless}, {innumerable},

{innumerous}, {myriad(a)}, {multitudinous}, {numberless},

{uncounted}, {unnumberable}, {unnumbered}, {unnumerable}]

4: total and all-embracing; "God's infinite wisdom"

infinite

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)