$\lim_{x\to a} f(x)=\lim_{h\to 0}f(a+h)$ versus $\lim_{x\to a} f(x)=\lim_{x\to 0}f(a+x)$ Just had a quick question about the variable naming observed in the following statement:

$\displaystyle\lim_{x\to a} f(x)=\displaystyle\lim_{h\to 0}f(a+h)$

Is the above statement equivalent to:
$\displaystyle\lim_{x\to a} f(x)=\displaystyle\lim_{x\to 0}f(a+x) \quad ?$
If so, is there any particular reason to prefer the former over the latter? Cheers~

The first form is safer, as it uses distinct variables for the absolute and relative positions, hence avoids confusions.
(A second argument is that "by tradition", $h$ is immediately recognized as a relative displacement.)
