|1.||(sometimes plural) the ultimate extent, degree, or amount of something: the limit of endurance|
|2.||(often plural) the boundary or edge of a specific area: the city limits|
|3.||(often plural) the area of premises within specific boundaries|
|4.||the largest quantity or amount allowed|
|a. 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|
|b. a value to which a sequence an approaches arbitrarily close as n approaches infinity|
|c. the limit of a sequence of partial sums of a convergent infinite series: the limit of |
|6.||maths one of the two specified values between which a definite integral is evaluated|
|7.||informal the limit a person or thing that is intolerably exasperating|
|a. out of bounds|
|b. forbidden to do or use: smoking was off limits everywhere|
|9.||within limits to a certain or limited extent: I approve of it within limits|
|—vb , -its, -iting, -ited|
|10.||to restrict or confine, as to area, extent, time, etc|
|11.||law to agree, fix, or assign specifically|
|[C14: from Latin līmes boundary]|
limit lim·it (lĭm'ĭt)
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.
|limit (lĭm'ĭt) Pronunciation Key
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.