-infinity-

n.; pl. Infinities [ L. infinitas; pref. in- not + finis boundary, limit, end: cf. F. infinité. 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 ]

☞ 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 ]