In mathematics, a limit is a value toward which an expression converges as one or more variables approach certain values. Limits are important in calculus and analysis.

Consider the limit of the expression 2 *x* + 3 as *x* approaches 0. It is not difficult to see that this limit is 3, because we can assign the value 0 to the variable *x* and perform the calculation directly. This sort of substitution is not possible, however, when we consider the limit of the expression 1/ *x* - 2 as *x* increases without limit. (The expression for this is ' *x* approaches infinity.') It is apparent that 1/ *x* approaches 0 as 1/ *x* approaches infinity, although we cannot directly substitute infinity for *x* and calculate 1/ *x* = 0. The limit, as *x* approaches infinity, of 1/ *x* - 2 is therefore equal to -2.

These expressions would be denoted in mathematical literature as follows:

The term 'limit' is symbolized 'Lim.' The arrow means 'approaches.' Infinity is symbolized by the sideways 8.

Also see infinity and Mathematical Symbols .

*This was last updated in*September 2005

*Posted by:*Margaret Rouse

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