- 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.
verb (used with object)
Origin of limit
Synonyms for limit
- 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
- out of bounds
- forbidden to do or usesmoking was off limits everywhere
verb -its, -iting or -ited (tr)
Word Origin for limit
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.
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]
see go whole hog (the limit); sky's the limit; the limit.