infinite

American Heritage® Dictionary of the English Language, Fourth Edition

1. adj. Having no boundaries or limits.
2. adj. Immeasurably great or large; boundless: infinite patience; a discovery of infinite importance.
3. adj. Mathematics Existing beyond or being greater than any arbitrarily large value.
4. adj. Mathematics Unlimited in spatial extent: a line of infinite length.
5. adj. Mathematics Of or relating to a set capable of being put into one-to-one correspondence with a proper subset of itself.
6. n. Something infinite.

Century Dictionary and Cyclopedia

1. Immeasurably or innumerably great; so great as to be absolutely incapable of being measured or counted. Space is the most familiar example of an object ordinarily conceived to be infinite. Anaximander and other early Greek philosophers appear to have called this ἅπειρον, unbounded, and the Latin infinitum is a translation of this Greek word. The two ideas, that of the immeasurable and that of the unbounded, were confused by the early Greeks, and also by some modern philosophers, as Hobbes and Hegel. Ordinary geometry regards space as both unbounded and immeasurable; but the hypothesis of modern geometers concerning the properties of space, called elliptic non-Euclidean geometry, makes space measurable (in that it supposes that a point proceeding along a straight line, after having traversed a vast but finite distance, would return from behind to its original starting-point), and this supposition, which is entirely self-consistent, leaves space unbounded just as the surface of a spherical body, such as a pea, or the circumference of a circle is unbounded. But it is no more the usage of ordinary language than of mathematics to call the surface of a pea infinite. On the other hand, geometers conceive that if from an unbounded and immeasurable (infinite) right line a small part be cut off, what remains, having two terminals, is bounded but immeasurable; and in ordinary as in mathematical language such a line would be called infinite. Thus, the usual and mathematical meaning of the word infinite departs from the suggestion of its etymology. Mathematicians speak of the ratios of infinite quantities; such an expression supposes that the arrangement of the units or elements remains essentially unchanged in the measurement. Thus, a line two inches long, comprising an infinity of point, may be said to have twice as many points as one which measures only one inch and also comprises an infinity of points: but this only means that the former multitude appears twice as great as the latter when the points are not completely disintegrated. So orders of infinity are spoken of. (See infinitesimal.) These expressions have led metaphysicians to suppose that the infinite quantity of the mathematicians is not the maximum, and consequently is not truly infinite. But the points of a line, however short, can be brought into a one-to-one correspondence with those of all space—that is, for every point in all space there is a distinct and separate point in the line, and that although the space considered have an infinite multitude of dimensions; so that the multitude of points in a line is the greatest possible quantity. Mathematicians distinguish, however, two kinds of infinity. The multitude of finite whole numbers may be said to be infinite, since the counting of them cannot be completed. But the multitude of points upon a line, which corresponds to the multitude of numbers expressible by an infinite series of decimals, is infinitely greater, in that it cannot be brought into a one-to-one correspondence with the former. If ∞ represents the former multitude, 10 will represent the latter, so that the former is analogous to a logarithmic infinite, or infinite of order zero. The former is said to be improperly or discretely infinite, the latter properly or continuously infinite.
2. All-embracing; lacking nothing; the greatest possible; perfect; absolute: applied only to Divinity.
3. Boundless; unbounded; endless; without limit; interminable. In this sense the surface of a pea is infinite, while a plane of immeasurable extent whose continuity is interrupted by one small hole is finite.
4. By hyperbole, indefinitely extensive; beyond our powers of measuring or reckoning.
5. [Tr. Gr. ἀόριστος: see aorist.] In logic, modified, as a term, by a sign of negation.
6. n. Anything which is infinite, in any sense. Specifically— [cap. or lowercase] In philosophy, the Infinite Being; the absolute Deity.
7. n. A large number; a crowd.
8. n. In geometry, the plane on which lie all points at infinity and all straights at infinity.

Wiktionary

1. adj. set theory, of a set Having infinitely many elements.
2. n. Infinitely many.

GNU Webster's 1913

1. adj. Unlimited or boundless, in time or space.
2. adj. Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; ; -- opposed to finite.
3. adj. Indefinitely large or extensive; great; vast; immense; gigantic; prodigious.
4. adj. (Math.) Greater than any assignable quantity of the same kind; -- said of certain quantities.
5. adj. (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.
6. n. That which is infinite; boundless space or duration; infinity; boundlessness.
7. n. (Math.) An infinite quantity or magnitude.
8. n. An infinity; an incalculable or very great number.
9. n. The Infinite Being; God; the Almighty.

WordNet 3.0

1. adj. total and all-embracing
2. adj. too numerous to be counted
3. adj. having no limits or boundaries in time or space or extent or magnitude
4. n. the unlimited expanse in which everything is located
5. adj. of verbs; having neither person nor number nor mood (as a participle or gerund or infinitive)