# 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.

References in classic literature ?
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.
I'll be married in this lilac gingham: you may make a dressing-gown for yourself out of the pearl-grey silk, and an infinite series of waistcoats out of the black satin.
Thee Father first they sung Omnipotent, Immutable, Immortal, Infinite, Eternal King; thee Author of all being, Fountain of Light, thy self invisible Amidst the glorious brightness where thou sit'st Thron'd inaccessible, but when thou shad'st The full blaze of thy beams, and through a cloud Drawn round about thee like a radiant Shrine, Dark with excessive bright thy skirts appeer, Yet dazle Heav'n, that brightest Seraphim Approach not, but with both wings veil thir eyes.
And, yet, a feeling of infinite regret came over him, as he thought of her lying at his feet sobbing like a little child.
The INFINITE DIVISIBILITY of matter, or, in other words, the INFINITE divisibility of a FINITE thing, extending even to the minutest atom, is a point agreed among geometricians, though not less incomprehensible to common-sense than any of those mysteries in religion, against which the batteries of infidelity have been so industriously leveled.
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.
My friends," said I, "we are bound one to the other for ever, and I am under infinite obligations to you.
Moreau stopped, facing this creature, who cringed towards him with the memory and dread of infinite torment.
Both Buddha and Lao Tzu are poets, one listening to the rhythm of infinite sorrow, one to the rhythm of infinite joy.
Such men, for the reasons given, can open the way into the state and render the victory easy; but if you wish to hold it afterwards, you meet with infinite difficulties, both from those who have assisted you and from those you have crushed.
Do not repeat the tactics which have gained you one victory, but let your methods be regulated by the infinite variety of circumstances.
The encouragers of the first mob never intended matters should go this length, and the people in general expressed the utter detestation of this unparalleled outrage, and I wish they could be convinced what infinite hazard there is of the most terrible consequences from such demons, when they are let loose in a government where there is not constant authority at hand sufficient to suppress them.

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