Notation concerning $x \rightarrow y$

Question

First of all, does $x \rightarrow y\ $ have a specific name? In limits we would say " .. as $x$ approaches $y$ " .

Second point, $\lim_{x\rightarrow 0} 3+x=3$ if we remove the limit and just consider $3 + x$ such that $x \rightarrow 0$ is it still correct to equate the operation to $3$ or should we write $3+x \rightarrow 3$ (i.e $3+x = 3.0000...1$)? If so, how should it be written? $x \rightarrow 0, 3+x \rightarrow 3$ ?

Answer 1

It is commonly written "$3+x \to 3$ as $x \to 0$."