infinity

Definitions

  • WordNet 3.6
    • n infinity time without end
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Webster's Revised Unabridged Dictionary
    • Infinity (Math) A quantity greater than any assignable quantity of the same kind.
    • Infinity Endless or indefinite number; great multitude; as an infinity of beauties.
    • Infinity (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.
    • Infinity Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
    • Infinity Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity. "There can not be more infinities than one; for one of them would limit the other."
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Century Dictionary and Cyclopedia
    • n infinity The condition of being infinite or the greatest possible; immeasurableness; innumerability; perfection: as, the infinity of God; infinity of duration.
    • n infinity Unlimited extension; figuratively, exhaustless quantity or number: as, inconceivable infinity; an infinity of details.
    • n infinity 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.
    • n infinity An infinite number: as, an infinity of straight lines. Its symbol is ∞.
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Chambers's Twentieth Century Dictionary
    • ns Infinity boundlessness: immensity: countless or indefinite number
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Quotations

  • Samuel Taylor Coleridge
    Samuel%20Taylor%20Coleridge
    “The principle of the Gothic architecture is infinity made imaginable.”
  • William Blake
    William%20Blake
    “To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hand, and eternity in an hour.”
  • Alfred Jarry
    Alfred Jarry
    “God is the tangential point between zero and infinity.”
  • Jacques Maritain
    Jacques Maritain
    “A single idea, if it is right, saves us the labor of an infinity of experiences.”
  • Joseph Brodsky
    Joseph%20Brodsky
    “The poetic notion of infinity is far greater than that which is sponsored by any creed.”
  • Edgar Quinet
    Edgar%20Quinet
    “I mistrust the satisfaction which makes a display of the possession of Infinity; that is called fatuity in philosophic terms.”

Etymology

Webster's Revised Unabridged Dictionary
L. infinitas,; pref. in-, not + finis, boundary, limit, end: cf. F. infinité,. See Finite

Usage

In literature:

The lower courses then stretch seemingly into infinity to right and left, while the summit soars up out of our sight into the sky.
"History Of Egypt, Chaldæa, Syria, Babylonia, and Assyria, Volume 2 (of 12)" by G. Maspero
To quarrel now, indeed, requires an infinity of patience.
"Certain Personal Matters" by H. G. Wells
The idea of infinity is for us in idea without model, without prototype, without object.
"Superstition In All Ages (1732)" by Jean Meslier
You are the infinity of the unmitigated, the supreme of the superfluous.
"Olympian Nights" by John Kendrick Bangs
Arnold took it delicately in his own thin fingers to examine it; an infinity of contrast rested in the touch.
"Hilda" by Sarah Jeanette Duncan
This impassioned taste for infinity and pious sentiment continued their influences over her after her return to her father's house.
"History of the Girondists, Volume I" by Alphonse de Lamartine
Usually with the infin.
"Latin for Beginners" by Benjamin Leonard D'Ooge
For who doubts that geometry, for instance, has an infinite infinity of problems to solve?
"Pascal's Pensées" by Blaise Pascal
Infinity, a source of the sublime, i.
"The Works of the Right Honourable Edmund Burke, Vol. XII. (of XII.)" by Edmund Burke
To be floating in that infinity of blue water would be better than this.
"Old Kaskaskia" by Mary Hartwell Catherwood
Out of the corner of my eye I saw Lezard fold his arms and sit frowning at infinity.
"Police!!!" by Robert W. Chambers
And first would come the vastness of the sea, which prompts vague intuitions of mystery and infinity.
"Nature Mysticism" by J. Edward Mercer
There are also precious stones, pearls, and an infinity of spices.
"The Northmen, Columbus and Cabot, 985-1503" by Various
That an infinity of paper will not produce an infinity of food.
"The Life of George Washington, Vol. 5 (of 5)" by John Marshall
Infinity, absolute infinity, is impracticable in any German metre.
"The Uncollected Writings of Thomas de Quincey--Vol. 1" by Thomas de Quincey
I saw then that his eyes, although they looked straight at her, were focused beyond her for infinity.
"Caves of Terror" by Talbot Mundy
Great circling patches of mist rose up from below and added a sense of infinity to its depths.
"The Triumph of John Kars" by Ridgwell Cullum
Because of all this, this all, which hath an infinity in it, the Lord God hath made with us a sure covenant.
"The Covenants And The Covenanters" by Various
And as it is with extension, so it is with mind, which is also infinite with the infinity of its object.
"Short Studies on Great Subjects" by James Anthony Froude
All three stared into the plate, seeing only an infinity of emptiness, marked only by the infinitely remote and coldly brilliant stars.
"Triplanetary" by Edward Elmer Smith
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In poetry:

Then only in the empty spaces,
Death, walking very silently,
Shall fear the glory of our faces
Through all the dark infinity.
"The Call" by Rupert Brooke
O Space and Time and stars at strife,
How dreadful your infinity!
Shrined by your termless trinity,
How strange, how terrible, is life!
"The Testimony of the Suns" by George Sterling
Among the sons of an accursed century
I took my place at the irreverent table,
Where still was heard, under all the revel,
The moan of a helpless thirst for infinity.
"The Convert" by Antero Tarquinio de Quental
From point to point, over there, the distant lights,
And in the sky, above, dreadful voices
Coming and going from the infinity of the marshes and planes
To the infinity of the valleys and the woods.
"Infinitely" by Emile Verhaeren
I learned not to fear infinity,
The far field, the windy cliffs of forever,
The dying of time in the white light of tomorrow,
The wheel turning away from itself,
The sprawl of the wave,
The on-coming water.
"The Far Field" by Theodore Roethke
Shining in dim transparence, the whole of infinity lies
Behind the veils that the finger of radiant winter weaves;
And down on us falls the foliage of star in glittering sheaves,
From out the depths of the forest, the forest obscure of the skies.
"The Glory Of The Heavens" by Emile Verhaeren

In news:

From Mayapple Salon and Boutique's own Roxie Hunt, here is an Infinity Braid tutorial featuring Brooke Boatright.
Affiliates of US Joiner ("US Joiner") announced today the acquisition of Infinity Offshore Marine, LLC (" Infinity ").
Years late, but it's still worth taking a look at the landmark iOS game ' Infinity Blade.
Avolites Media's Groundbreaking Sapphire Media Infinity Wins Coveted Innovation Award at PLASA 2012.
The Avolites Media Sapphire Media Infinity video control system has been awarded the prestigious PLASA Award for Innovation.
View to Infinity ,' at Neue Galerie.
Ferdinand Hodler, "View to Infinity ".
Much like 2010's Omni, Minus The Bear's latest release, Infinity Overhead, should come with a warning label.
For young readers who are also gamers, 'The Infinity Ring' series from Scholastic offers a chance to interact with history through a role-playing video game.
Scholastic's ' Infinity Ring' a multimedia ride through history.
To say a thousand and one nights is to add one to infinity .
Getloaded, an Internet-based logistics freight matching site, is now integrating its software with McLeod Software and Infinity Software Solutions, two large transportation technology players.
I'm Nick Eliopulos, editor of the new series Infinity Ring which launches on August 28th.
Infinity Ring is a fun, action-packed time-travel adventure.
Kptm.com Thor Purchases Bus Assets Of Krystal Infinity , LLC.
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In science:

To make it more convincing now let us assume that the velocity v is very high, say is near to infinity, so that even if the real rest mass of the particle is very high its relative mass at v will be small.
On a heuristic point regarding the origin of tachyons and a revamped definition for them
The velocity = v/c is the velocity the particle would have “at infinity” as measured by the (stationary) observer at infinity.
Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics
Note dτ/dε approaches infinity as E approaches 1 and ε approaches 0, the point corresponding to the stationary observer at infinity.
Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics
This is consistent with a particle starting at rest at infinity.
Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics
By (2.18), the solution of this equation is to be subject to the condition that us(xs) → 1 as the magnitude of all differences rj – rk tends to infinity, that is, as Us(xs) → 0.
A new view on superfluidity
It has Planck limits. Not only energy but also space seems quantized at Plank limits, and loop quantum gravity theory uses discrete space to avoid mathematical infinities (Smolin, 2001).
The emergence of the physical world from information processing
Its energy does not reach infinity, despite the infinite number of passes, because of a defocusing of the light .
The Universal Arrow of Time III-IV:(Part III) Nonquantum gravitation theory (Part IV) Quantum gravitation theory
We now see what happens when l, m, n go to infinity ble with it (see ). This result plus the elusiveness Fix l, m and let n » l.
Instrumentality Tests Revisited
Therefore, the simple form of spherical wave ASF in Eq. (8) is not valid in this case since the first integral in Eq. (6) cannot be extended to infinity.
Atomic Scattering Factor for a Spherical Wave and the Near Field Effects in X-ray Fluorescence Holography
But a boundary condition is a boundary condition, even if the boundary is at infinity.
Cosmology from the Top Down
Another deep concern with the unitary representation of the Poincaré group framework is the appearance of the infinities.
Canonically relativistic quantum mechanics: Casimir field equations of the quaplectic group
There is a considerable body of literature associated with theories with a maximal acceleration, as for example described in the references of . One of the goals is to address the infinities encountered in the quantum theories. One of the most notable of these is as it seeks to provide a deep geometric foundation.
Canonically relativistic quantum mechanics: Casimir field equations of the quaplectic group
G(t) grows quadratically with time, never reaching a pole: it is dynamically suppressing its own infinities.
A Scenario for Strong Gravity without Extra Dimensions
It results in the infinity of the losses of the energy used for radiation of the internal waves and for the wave resistance.
General problems of the internal gravity waves linear theory
The peculiarities of the exchange of information via light signals, between the observers mentioned above, are generated by the fact that after a very long time of motion theirs velocities tend to infinity without reaching it.
The system of uniformly accelerating observers
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