Editing Limit of a function (section)

=== In terms of nearness ===
At the 1908 international congress of mathematics [[Frigyes Riesz|F. Riesz]] introduced an alternate way defining limits and continuity in concept called "nearness".<ref>{{citation|contribution=Stetigkeitsbegriff und abstrakte Mengenlehre (The Concept of Continuity and Abstract Set Theory)|author=F. Riesz|date=7 April 1908|title=[[International Congress of Mathematicians|1908 International Congress of Mathematicians]]}}</ref> A point {{mvar|x}} is defined to be near a set <math>A\subseteq \R</math> if for every {{math|''r'' > 0}} there is a point {{math|''a'' &in; ''A''}} so that {{math|{{abs|''x'' &minus; ''a''}} < ''r''}}.  In this setting the 
<math display=block>\lim_{x\to a} f(x)=L</math>
if and only if for all <math>A\subseteq \R,</math> {{mvar|L}} is near {{math|''f''(''A'')}} whenever {{mvar|a}} is near {{mvar|A}}.
Here {{math|''f''(''A'')}} is the set <math>\{f(x) | x \in A\}.</math>  This definition can also be extended to metric and topological spaces.