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Webster 1913 Edition


Infinity

In-fin′i-ty

,
Noun.
;
pl.
Infinities
(#)
.
[L.
infinitas
; pref.
in-
not +
finis
boundary, limit, end: cf. F.
infinité
. 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. Raleigh.
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.
☞ 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
.

Webster 1828 Edition


Infinity

INFIN'ITY

,
Noun.
[L. infinitas.]
1.
Unlimited extent of time, space or quantity; boundlessness. We apply infinity to God and his perfections; we speak of the infinity of his existence, his knowledge, his power, his goodness and holiness.
2.
Immensity; indefinite extent.
3.
Endless or indefinite number; a hyperbolical use of the word; as an infinity of beauties.

Definition 2021


infinity

infinity

English

Noun

infinity (countable and uncountable, plural infinities)

  1. (uncountable) Endlessness, unlimitedness, absence of a beginning, end or limits to size.
  2. (countable, mathematics) A number that has an infinite numerical value that cannot be counted.
    • 2012 January 1, Michael Riordan, “Tackling Infinity”, in American Scientist, volume 100, number 1, page 86:
      Some of the most beautiful and thus appealing physical theories, including quantum electrodynamics and quantum gravity, have been dogged for decades by infinities that erupt when theorists try to prod their calculations into new domains. Getting rid of these nagging infinities has probably occupied far more effort than was spent in originating the theories.
  3. (countable, topology, analysis) An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.
  4. (uncountable) 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.
  5. (uncountable) The symbol .

Usage notes

In mathematics there are several different infinities; see transfinite.

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