Infinitesimal calculus, the different and the integral calculus, when developed according to the method used by Leibnitz, who regarded the increments given to variables as infinitesimal.

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

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

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.

Infinitely
(In"fi*nite*ly), adv.

1. Without bounds or limits; beyond or below assignable limits; as, an infinitely large or infinitely small quantity.

2. Very; exceedingly; vastly; highly; extremely. "Infinitely pleased." Dryden.

Infiniteness
(In"fi*nite*ness), n. The state or quality of being infinite; infinity; greatness; immensity. Jer. Taylor.

Infinitesimal
(In`fin*i*tes"i*mal) a. [Cf. F. infinitésimal, fr. infinitésime infinitely small, fr. L. infinitus. See Infinite, a.] Infinitely or indefinitely small; less than any assignable quantity or value; very small.


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