| Limit Of A Function |
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In Mathematics , the limit of a function is a fundamental concept in Mathematical Analysis . Rather informally, to say that a function ''f'' has limit ''L'' at a point ''p'', is to say that we can make the value of ''f'' as close to ''L'' as we want, by taking points close enough to ''p''. Formal definitions, first devised around the end of the 19th Century , are given below. See Net (topology) for a generalization of the concept of limit. HISTORY See Mathematical Analysis . FORMAL DEFINITION Functions on metric spaces Suppose ''f'' : (''M'',d''M'') -> (''N'',d''N'') is a map between two Metric Space s, ''p'' is a Limit Point of ''M'' and ''L''∈''N''. We say that the limit of ''f'' at ''p'' is ''L'' and write : If And Only If for every ε > 0 there exists a δ > 0 such that for all ''x''∈''M'' with 0 < d''M''(''x'', ''p'') < δ, we have d''N''(''f''(''x''), ''L'') < ε. Real-valued functions |
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