The Collaborative International Dictionary of English v.0.48:

Infinity \In*fin"i*ty\, n.; pl. Infinities. [L. infinitas;
   pref. in- not + finis boundary, limit, end: cf. F.
   infinit['e]. See Finite.]
   [1913 Webster]
   1. Unlimited extent of time, space, or quantity; eternity;
      boundlessness; immensity. --Sir T. More.
      [1913 Webster]

            There can not be more infinities than one; for one
            of them would limit the other.        --Sir W.
                                                  Raleigh.
      [1913 Webster]

   2. Unlimited capacity, energy, excellence, or knowledge; as,
      the infinity of God and his perfections. --Hooker.
      [1913 Webster]

   3. Endless or indefinite number; great multitude; as an
      infinity of beauties. --Broome.
      [1913 Webster]

   4. (Math.) A quantity greater than any assignable quantity of
      the same kind.
      [1913 Webster]

   Note: Mathematically considered, infinity is always a limit
         of a variable quantity, resulting from a particular
         supposition made upon the varying element which enters
         it. --Davies & Peck (Math. Dict.).
         [1913 Webster]

   5. (Geom.) 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.
      [1913 Webster]

   Circle at infinity, an imaginary circle at infinity,
      through which, in geometry of three dimensions, every
      sphere is imagined to pass.

   Circular points at infinity. See under Circular.
      [1913 Webster]

WordNet (r) 3.0 (2006):

infinity
    n 1: time without end [syn: eternity, infinity]

Moby Thesaurus II by Grady Ward, 1.0:

153 Moby Thesaurus words for "infinity":
   Gaussian integer, aesthetic distance, algebraic number, ampleness,
   amplitude, astronomical number, billion, boundlessness, bulk,
   cardinal, cardinal number, ceaselessness, clearance, coeternity,
   compass, complex number, constancy, continualness, continuance,
   deep space, defective number, depths of space, distance,
   divergence, durability, endlessness, enormity, enormousness,
   eternalness, eternity, even number, ever-duringness,
   everlastingness, everness, everywhereness, expanse, extension,
   extent, farness, finite number, foreverness, formidableness,
   fraction, fullness, gigantism, glory, googol, googolplex, grandeur,
   grandness, great scope, greatness, holiness, hugeness,
   imaginary number, immensity, immutability, impair, incessancy,
   indestructibility, infinite duration, infinite goodness,
   infinite justice, infinite love, infinite mercy, infinite power,
   infinite wisdom, infinitude, integer, intensity, interminability,
   irrational, irrational number, jillion, large number, largeness,
   leeway, length, lengthiness, light, light-years, linear measures,
   long time, longitude, longness, magnitude, majesty, margin,
   measure, might, mightiness, mileage, mixed number, muchness,
   never-endingness, omnipotence, omnipotency, omnipresence,
   omniscience, omnisciency, ordinal, overall length, pair, parsecs,
   perdurability, perenniality, perennialness, permanence,
   perpetualness, perpetuity, perspective, piece, plenitude,
   polygonal number, power, prime number, prodigiousness,
   pure imaginary, range, rational, rational number, reach, real,
   real number, rectangular number, remoteness, round number,
   sempiternity, separation, serial number, sovereignty, space, span,
   stability, strength, stretch, stride, stupendousness, surd,
   timelessness, transcendental number, transfinite number,
   tremendousness, trillion, ubiquity, unceasingness, unity, vastness,
   way, ways, whole number, yardage, zillion



The Jargon File (version 4.4.7, 29 Dec 2003):

infinity
 n.

    1. The largest value that can be represented in a particular type of
    variable (register, memory location, data type, whatever).

    2. minus infinity: The smallest such value, not necessarily or even usually
    the simple negation of plus infinity. In N-bit twos-complement arithmetic,
    infinity is 2^N-1 - 1 but minus infinity is - (2^N-1), not -(2^N-1 - 1).
    Note also that this is different from time T equals minus infinity, which
    is closer to a mathematician's usage of infinity.


The Free On-line Dictionary of Computing (30 December 2018):

infinity

   1.  The size of something infinite.

   Using the word in the context of sets is sloppy, since
   different infinite sets aren't necessarily the same size
   cardinality as each other.

   See also aleph 0

   2.  The largest value that can be represented in
   a particular type of variable (register, memory location,
   data type, whatever).

   See also minus infinity.

   [Jargon File]

   (1994-11-18)