infinity

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The quality or condition of being infinite.
2. n. Unbounded space, time, or quantity.
3. n. An indefinitely large number or amount.
4. n. Mathematics The limit that a function ∫ is said to approach at x = a when ∫(x) is larger than any preassigned number for all x sufficiently near a.
5. n. A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel.
6. n. A distance setting, as on a camera, beyond which the entire field is in focus.

Century Dictionary and Cyclopedia

1. n. The condition of being infinite or the greatest possible; immeasurableness; innumerability; perfection: as, the infinity of God; infinity of duration.
2. n. Unlimited extension; figuratively, exhaustless quantity or number: as, inconceivable infinity; an infinity of details.
3. n. In geometry, the part of space at an infinite distance from the part chiefly considered. Owing to the mechanical properties of the straight line, the most important mode of geometrical transformation is that which transforms every straight line into a straight line, its position only being changed. But this transforms the part of space at infinity into a plane, just as in a perspective view of an unbounded plane the infinitely distant parts are compressed into a line. Hence, mathematicians generally speak of the plane at infinity, or the line at infinity in a plane. In analytical geometry the plane at infinity is best considered as two coincident planes, fastened together at an imaginary nodal circle, and constituting a degenerate sphere, called the sphere at infinity. (See absolute, n., 2.) In the theory of functions, the most important mode of transformation of the plane is one which preserves the magnitudes of all angles, and this transforms the infinitely distant parts of the plane into a point; hence, in that branch of mathematics, the point at infinity is spoken of.
4. n. An infinite number: as, an infinity of straight lines. Its symbol is ∞.

Wiktionary

1. n. Limitlessness, unlimitedness, something which is growing without limits or bounds.
2. n. A number that has an infinite numerical value that cannot be counted.
3. n. A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further.
4. n. The symbol ∞.

GNU Webster's 1913

1. n. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
2. n. Unlimited capacity, energy, excellence, or knowledge.
3. n. Endless or indefinite number; great multitude; as an infinity of beauties.
4. n. A quantity greater than any assignable quantity of the same kind.
5. n. That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.

WordNet 3.0

1. n. time without end