Why does $(x \to a) ≠ (x = a)$ , But $f(x \to a) = f(x = a)$ I am really satisfied that $(x \to a) ≠(x=a)$ and if that is not right , Then all the process of $Limits$ is dividing by zero and that is a crime.
Since $(x \to a) + h = (x=a)$ , $h ≠ 0$,So Why does $f(x \to a) = f(x = a)$ ?
NOTE:I am talking about continuous function.

Your question seems unclear, but perhaps emphasizing this distinction will help:
A function $f: \mathbb R \longrightarrow \mathbb R$ is continuous at $a \in \mathbb R$ if (and only if) for every $\varepsilon>0$ there exists $\delta>0$ such that $|f(x)-f(a)|<\varepsilon$ whenever $|x-a|<\delta$.
We write $\lim_{x \to a} f(x)=L$ if and only if for every $\varepsilon>0$ there exists $\delta>0$ such that $|f(x)-L|<\varepsilon$ whenever $0<|x-a|<\delta$.
Noticing the differences between the two formal definitions, we see that a function $f$ is continuous at $a \in \mathbb R$ if and only if $\lim_{x \to a} f(x)=f(a)$.
