1. [adj]  total and all-embracing; "God's infinite wisdom"
2. [adj]  too numerous to be counted; "incalculable riches"; "countless hours"; "an infinite number of reasons"; "innumerable difficulties"; "the multitudinous seas"; "myriad stars"; "untold thousands"
3. [adj]  having no limits or boundaries in time or space or extent or magnitude; "the infinite ingenuity of man"; "infinite wealth"
4. [adj]  (grammar) of verbs; having neither person nor number nor mood (as a participle or gerund or infinitive); "infinite verb form"

1. \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.
   
   

2. \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.
   
   

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]