Editing Continuous function (section)

====Definition in terms of limits of functions====
The function {{math|''f''}} is ''continuous at some point'' {{math|''c''}} of its domain if the [[limit of a function|limit]] of <math>f(x),</math> as ''x'' approaches ''c'' through the domain of ''f'',  exists and is equal to <math>f(c).</math><ref>{{Citation | last1=Lang | first1=Serge | author1-link=Serge Lang | title=Undergraduate analysis | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | series=[[Undergraduate Texts in Mathematics]] | isbn=978-0-387-94841-6 | year=1997}}, section II.4</ref> In mathematical notation, this is written as
<math display="block">\lim_{x \to c}{f(x)} = f(c).</math>
In detail this means three conditions: first, {{math|''f''}} has to be defined at {{math|''c''}} (guaranteed by the requirement that {{math|''c''}} is in the domain of {{math|''f''}}). Second, the limit of that equation has to exist. Third, the value of this limit must equal <math>f(c).</math>

(Here, we have assumed that the domain of ''f'' does not have any [[isolated point]]s.)