infinite


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Related to infinite: Infinite set

infinite

Maths
a. having an unlimited number of digits, factors, terms, members, etc.
b. (of a set) able to be put in a one-to-one correspondence with part of itself
c. (of an integral) having infinity as one or both limits of integration

infinite

[′in·fə·nət]
(mathematics)
Larger than any fixed number.

infinite

(mathematics)
1. Bigger than any natural number. There are various formal set definitions in set theory: a set X is infinite if

(i) There is a bijection between X and a proper subset of X.

(ii) There is an injection from the set N of natural numbers to X.

(iii) There is an injection from each natural number n to X.

These definitions are not necessarily equivalent unless we accept the Axiom of Choice.

2. The length of a line extended indefinitely.

See also infinite loop, infinite set.
References in classic literature ?
Some may wonder how it can happen that Agathocles, and his like, after infinite treacheries and cruelties, should live for long secure in his country, and defend himself from external enemies, and never be conspired against by his own citizens; seeing that many others, by means of cruelty, have never been able even in peaceful times to hold the state, still less in the doubtful times of war.
They were renewed by love; the heart of each held infinite sources of life for the heart of the other.
They had another seven years to wait, and what terrible suffering and what infinite happiness before them
But these recollections scarcely troubled him now; he knew with what infinite love he would now repay all her sufferings.
On this Friday she buried her face in the blooming geraniums on Miss Maxwell's plant-stand, selected Romola from one of the bookcases, and sank into a seat by the window with a sigh of infinite content, She glanced at the clock now and then, remembering the day on which she had been so immersed in David Copperfield that the Riverboro train had no place in her mind.
The middle one of the three windows was half-way open; and sitting close beside it, taking the air with an infinite sadness of mien, like some disconsolate prisoner, Utterson saw Dr.
For what is the array of the strongest ropes, the tallest spars and the stoutest canvas against the mighty breath of the infinite, but thistle stalks, cobwebs and gossamer?
which way shall I flie Infinite wrauth, and infinite despaire?
But thou hast promis'd from us two a Race To fill the Earth, who shall with us extoll Thy goodness infinite, both when we wake, And when we seek, as now, thy gift of sleep.
So judge thou still, presumptuous, till the wrauth, Which thou incurr'st by flying, meet thy flight Seavenfold, and scourge that wisdom back to Hell, Which taught thee yet no better, that no pain Can equal anger infinite provok't.
But if we did not know that all which we possess of real and true proceeds from a Perfect and Infinite Being, however clear and distinct our ideas might be, we should have no ground on that account for the assurance that they possessed the perfection of being true.
Cabin-boy at twelve, ship's boy at fourteen, ordinary seamen at sixteen, able seaman at seventeen, and cock of the fo'c'sle, infinite ambition and infinite loneliness, receiving neither help nor sympathy, I did it all for myself--navigation, mathematics, science, literature, and what not.