infinite

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Related to infinitely: Infinitely small

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 ?
This was elevation for the species, and gave a dignity to my position, with which I am infinitely satisfied.
To destroy our malefactors piece-meal, drying up in their veins, drop by drop, the blood we are too chicken-hearted to shed by a single blow which would at once put a period to their sufferings, is deemed to be infinitely preferable to the old-fashioned punishment of gibbeting--much less annoying to the victim, and more in accordance with the refined spirit of the age; and yet how feeble is all language to describe the horrors we inflict upon these wretches, whom we mason up in the cells of our prisons, and condemn to perpetual solitude in the very heart of our population.
She was feeling, thinking, trembling about everything; agitated, happy, miserable, infinitely obliged, absolutely angry.
His passage across my field of vision was like that of other figures of that time: not to be forgotten, a little fantastic, infinitely enlightening for my contempt, darkening for my memory which struggles still with the clear lights and the ugly shadows of those unforgotten days.
The short ceremony was infinitely dreadful in the cold gray morning.
The chief reason was a sudden, vivid sense of the terrible contrast between something infinitely great and illimitable within him and that limited and material something that he, and even she, was.
He saw that life itself infinitely outvalued anything that could be feigned about it, but its richness seemed to corrupt him, and he had not the clear, ethical conscience which forced George Eliot to be realistic when probably her artistic prepossessions were romantic.
It was enough that the golden treasure buried upon the site of the burned bungalow was infinitely more valuable than any ransom that would have occurred even to the avaricious mind of the Arab, and if Werper could persuade the raider to share even a portion of it with him he would be well satisfied.
One thing he knew with absolute certitude: "Ephemera" was infinitely greater than anything he had done.
The theory is something like this: Space is pervaded by luminiferous ether, which is a material thing--as much a substance as air or water, though almost infinitely more attenuated.
She said, she could not help agreeing with her brother, that there was some merit in the sincerity of her confession, and in her integrity to her lover: that she had always thought her a very good girl, and doubted not but she had been seduced by some rascal, who had been infinitely more to blame than herself, and very probably had prevailed with her by a promise of marriage, or some other treacherous proceeding.
It was quite as good as an Insolvent Act, and infinitely more genteel.