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Suppose a function is defined by
\[f(x)= \left\{ \begin{array}{c} x \; x \lt 0 \\ 1 \; x=0 \\ x \; x \gt 0 \end{array} \right. \]

We can define the limit of a function  
\[f(x)\]
  at a point  
\[x_0\]
  in two ways - as  
\[x\]
  tends to  
\[x_0\]
  from below, written  
\[x \rightarrow x_0^{{}-{}}\]
  and as  
\[x\]
  tends to  
\[x_0\]
  from above, written  
\[x \rightarrow x_0^{{}+{}}\]
.  
\[f(x)\]
  is continuous at  
\[x_0\]
  if and only if  
\[lim_{x \rightarrow x_0^{{}-{}}} f(x)= lim_{x \rightarrow x_0^{{}+{}}} f(x)\]
.
As  
\[x \rightarrow 0^{{}-{}}\]
,  
\[f(x) =x \rightarrow 0\]
  and as  
\[x \rightarrow 0^{{}+{}}\]
,  
\[f(x) =x \rightarrow 0\]
  so  
\[f(x)\]
  is continuous at  
\[x=0\]
.