# Infinite

[in-fuh-nit] /ˈɪn fə nɪt/

**adjective**

1.

immeasurably great:

an infinite capacity for forgiveness.

2.

indefinitely or exceedingly great:

infinite sums of money.

3.

unlimited or unmeasurable in extent of space, duration of time, etc.:

the infinite nature of outer space.

4.

unbounded or unlimited; boundless; endless:

God’s infinite mercy.

5.

Mathematics.

**noun**

6.

something that is infinite.

7.

Mathematics. an infinite quantity or magnitude.

8.

the boundless regions of space.

9.

the Infinite (Being) God.

/ˈɪnfɪnɪt/

**adjective**

1.

2.

extremely or immeasurably great or numerous: infinite wealth

3.

all-embracing, absolute, or total: God’s infinite wisdom

4.

(maths)

**adj.**

late 14c., “eternal, limitless,” also “extremely great in number,” from Old French infinit “endless, boundless,” and directly from Latin infinitus “unbounded, unlimited,” from in- “not, opposite of” (see in- (1)) + finitus “defining, definite,” from finis “end” (see finish). The **noun** meaning “that which is infinite” is from 1580s.

infinite

(ĭn’fə-nĭt)

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.

[Jargon File]

(1995-03-29)

Tagged: i

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