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.]
1. Unlimited extent of time, space, or quantity; eternity;
boundlessness; immensity. --Sir T. More.
There can not be more infinities than one; for one
of them would limit the other. --Sir W.
2. Unlimited capacity, energy, excellence, or knowledge; as,
the infinity of God and his perfections. --Hooker.
3. Endless or indefinite number; great multitude; as an
infinity of beauties. --Broome.
4. (Math.) A quantity greater than any assignable quantity of
the same kind.
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.).
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.
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.