infinite

(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)

Source: The Free On-line Dictionary of Computing (27 SEP 03)
 

Infinite \In"fi*nite\, n.

1. That which is infinite; boundless space or duration; infinity; boundlessness. [1913 Webster]

Not till the weight is heaved from off the air, and the thunders roll down the horizon, will the serene light of God flow upon us, and the blue infinite embrace us again. --J. Martineau. [1913 Webster]

2. (Math.) An infinite quantity or magnitude. [1913 Webster]

3. An infinity; an incalculable or very great number. [1913 Webster]

Glittering chains, embroidered richly o'er With infinite of pearls and finest gold. --Fanshawe. [1913 Webster]

4. The Infinite Being; God; the Almighty. [1913 Webster]

Source: The Collaborative International Dictionary of English v.0.48
 

Infinite \In"fi*nite\, a. [L. infinitus: cf. F. infini. See In- not, and Finite.]

[1913 Webster]

1. Unlimited or boundless, in time or space; as, infinite duration or distance. [1913 Webster]

Whatever is finite, as finite, will admit of no comparative relation with infinity; for whatever is less than infinite is still infinitely distant from infinity; and lower than infinite distance the lowest or least can not sink. --H. Brooke. [1913 Webster]

2. Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite. [1913 Webster]

Great is our Lord, and of great power; his understanding is infinite. --Ps. cxlvii. 5. [1913 Webster]

O God, how infinite thou art! --I. Watts. [1913 Webster]

3. Indefinitely large or extensive; great; vast; immense; gigantic; prodigious. [1913 Webster]

Infinite riches in a little room. --Marlowe. [1913 Webster]

Which infinite calamity shall cause To human life. --Milton. [1913 Webster]

4. (Math.) Greater than any assignable quantity of the same kind; -- said of certain quantities. [1913 Webster]

5. (Mus.) Capable of endless repetition; -- said of certain forms of the canon, called also perpetual fugues, so constructed that their ends lead to their beginnings, and the performance may be incessantly repeated. --Moore (Encyc. of Music).

Syn: Boundless; immeasurable; illimitable; interminable; limitless; unlimited; endless; eternal. [1913 Webster]

Source: The Collaborative International Dictionary of English v.0.48
 

220 Moby Thesaurus words for "infinite": Atlantean, Brobdingnagian, Cyclopean, Gargantuan, Herculean, Homeric, abysmal, ageless, algorismic, algorithmic, aliquot, all-comprehensive, all-inclusive, all-knowing, all-powerful, all-present, all-seeing, all-wise, almighty, ample, amplitudinous, astronomic, astronomical, awesome, bottomless, boundless, broad, bulky, capacious, cardinal, ceaseless, changeless, coeternal, colossal, commodious, constant, continual, continuous, cosmic, countless, creating, creative, dateless, decimal, deep, differential, digital, elephantine, endless, enormous, epic, eternal, eternally the same, eterne, even, ever-being, ever-durable, ever-during, everlasting, everliving, everywhere, exhaustless, expansive, exponential, extended, extending, extending everywhere, extensive, far-reaching, figural, figurate, figurative, finite, fractional, galactic, giant, giantlike, gigantic, glorious, good, hallowed, heroic, highest, holy, huge, illimitable, illimited, imaginary, immeasurable, immemorial, immense, immortal, immutable, impair, impossible, incalculable, incessant, incomprehensible, indefinite, indestructible, indeterminable, indeterminate, inestimable, inexhaustible, infinitely continuous, innumerable, integral, interminable, interminate, irrational, jumbo, just, king-size, large, limitless, logarithmic, logometric, loving, luminous, majestic, making, mammoth, massive, massy, measureless, merciful, mighty, monster, monstrous, monumental, mountainous, multitudinous, negative, never-ceasing, never-ending, no end of, nonstop, nonterminating, nonterminous, numberless, numeral, numerary, numerative, numeric, numinous, odd, olamic, omnipotent, omnipresent, omniscient, one, ordinal, outsize, overgrown, pair, perdurable, permanent, perpetual, positive, possible, prime, prodigious, profound, radiant, radical, rational, real, reciprocal, roomy, sacred, sempiternal, shaping, shoreless, sizable, sovereign, spacious, spreading, steady, stupendous, submultiple, sumless, supreme, surd, termless, timeless, titanic, towering, transcendental, tremendous, ubiquitous, unbounded, unceasing, unchanging, uncircumscribed, uncountable, uncounted, undefined, undying, unending, unfathomable, unintermitting, uninterrupted, universal, unlimited, unmeasurable, unmeasured, unnumbered, unplumbed, unremitting, untold, vast, voluminous, weighty, wide, widespread, without bound, without end, without limit, without measure, without number

Source: Moby Thesaurus II by Grady Ward, 1.0
 

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: 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"

Source: WordNet (r) 2.0
 

Infinite \In"fi*nite\, a. [L. infinitus: cf. F. infini. See In- not, and Finite.]

1. Unlimited or boundless, in time or space; as, infinite duration or distance.

Whatever is finite, as finite, will admit of no comparative relation with infinity; for whatever is less than infinite is still infinitely distant from infinity; and lower than infinite distance the lowest or least can not sink. --H. Brooke.

2. Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.

Great is our Lord, and of great power; his understanding is infinite. --Ps. cxlvii. 5.

O God, how infinite thou art! --I. Watts.

3. Indefinitely large or extensive; great; vast; immense; gigantic; prodigious.

Infinite riches in a little room. --Marlowe.

Which infinite calamity shall cause To human life. --Milton.

4. (Math.) Greater than any assignable quantity of the same kind; -- said of certain quantities.

5. (Mus.) Capable of endless repetition; -- said of certain forms of the canon, called also perpetual fugues, so constructed that their ends lead to their beginnings, and the performance may be incessantly repeated. --Moore (Encyc. of Music).

Syn: Boundless; immeasurable; illimitable; interminable; limitless; unlimited; endless; eternal.

Source: Webster's Revised Unabridged Dictionary (1913)
 

Infinite \In"fi*nite\, n.

1. That which is infinite; boundless space or duration; infinity; boundlessness.

Not till the weight is heaved from off the air, and the thunders roll down the horizon, will the serene light of God flow upon us, and the blue infinite embrace us again. --J. Martineau.

2. (Math.) An infinite quantity or magnitude.

3. An infinity; an incalculable or very great number.

Glittering chains, embroidered richly o'er With infinite of pearls and finest gold. --Fanshawe.

4. The Infinite Being; God; the Almighty.

Source: Webster's Revised Unabridged Dictionary (1913)