# limit

[lim-it]

- the final, utmost, or furthest boundary or point as to extent, amount, continuance, procedure, etc.: the limit of his experience; the limit of vision.
- a boundary or bound, as of a country, area, or district.
- Mathematics.
- a number such that the value of a given function remains arbitrarily close to this number when the independent variable is sufficiently close to a specified point or is sufficiently large. The limit of 1/x is zero as x approaches infinity; the limit of (x − 1)2 is zero as x approaches 1.
- a number such that the absolute value of the difference between terms of a given sequence and the number approaches zero as the index of the terms increases to infinity.
- one of two numbers affixed to the integration symbol for a definite integral, indicating the interval or region over which the integration is taking place and substituted in a primitive, if one exists, to evaluate the integral.

- limits, the premises or region enclosed within boundaries: We found them on school limits after hours.
- Games. the maximum sum by which a bet may be raised at any one time.
- the limit, Informal. something or someone that exasperates, delights, etc., to an extreme degree: You have made errors before, but this is the limit.

- to restrict by or as if by establishing limits (usually followed by to): Please limit answers to 25 words.
- to confine or keep within limits: to limit expenditures.
- Law. to fix or assign definitely or specifically.

## Origin of limit^{}

1325–75; Middle English lymyt < Latin līmit- (stem of līmes) boundary, path between fields

## Synonyms

See more synonyms on Thesaurus.com2. confine, frontier, border. 8. restrain, bound.

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

# limit

- (sometimes plural) the ultimate extent, degree, or amount of somethingthe limit of endurance
- (often plural) the boundary or edge of a specific areathe city limits
- (often plural) the area of premises within specific boundaries
- the largest quantity or amount allowed
- maths
- a value to which a function f(x) approaches as closely as desired as the independent variable approaches a specified value (x = a) or approaches infinity
- a value to which a sequence a n approaches arbitrarily close as n approaches infinity
- the limit of a sequence of partial sums of a convergent infinite seriesthe limit of 1 + ½ + ¼ + ⅛ + … is 2

- maths one of the two specified values between which a definite integral is evaluated
- the limit informal a person or thing that is intolerably exasperating
- off limits
- out of bounds
- forbidden to do or usesmoking was off limits everywhere

- within limits to a certain or limited extentI approve of it within limits

- to restrict or confine, as to area, extent, time, etc
- law to agree, fix, or assign specifically

## Word Origin

C14: from Latin līmes boundary

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for the limit

# limit

# limit

### n.

c.1400, "boundary, frontier," from Old French limite "a boundary," from Latin limitem (nominative limes) "a boundary, limit, border, embankment between fields," related to limen "threshold." Originally of territory; general sense from early 15c. Colloquial sense of "the very extreme, the greatest degree imaginable" is from 1904.

Online Etymology Dictionary, © 2010 Douglas Harper

# limit

(lĭm′ĭt)

- The point, edge, or line beyond which something cannot or may not proceed.
- A confining or restricting object, agent, or influence.
- The greatest or least amount, number, or extent allowed or possible.

- To confine or restrict within a boundary or bounds.
- To fix definitely; to specify.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.

# limit

[lĭm′ĭt]

- A number or point for which, from a given set of numbers or points, one can choose an arbitrarily close number or point. For example, for the set of all real numbers greater than zero and less than one, the numbers one and zero are limit points, since one can pick a number from the set arbitrarily close to one or zero (even though one and zero are not themselves in the set). Limits form the basis for calculus, where a number L is defined to be the limit approached by a function f(x) as x approaches a if, for every positive number ε, there exists a number δ such that |;f(x)-L|; < ε if 0 < |;x-a|; < δ.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Idioms and Phrases with the limit

# the limit

The most extreme; someone or something that irritates, delights, or surprises to the ultimate degree. For example, Hiring and firing someone the same day—that's the limit in employee relations! or That excuse of yours for missing the wedding, that's the limit, or He's done wonders before but this last one is the limit. This idiom uses limit as “the last possible point or boundary.” [Colloquial; c. 1900]

# limit

The American Heritage® Idioms Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.