On Wiki they describe a condition for the composite limit rule:
$g$ does not take the value $b$ near $a$. That is, there exists a $\delta >0$ such that if $0<|x-a|<\delta$ then $|g(x)-b|>0$
This is mighty similar to a delta/epsilon limit, except instead of $<\epsilon$ it's $>0$. Is there a word for this, or is "does not take value near" the most common expression?