I am to find the proper number from $x \in \{2,3,4\}$ for which this following set is a neighborhood in $\mathbb{R}$ or in $\mathbb{C}$, $A:= \left] 1,4 \right[ \cap \left[ 2,5 \right]$
Firstly, I don't really understand what a neighborhood is. But what I understand till now is this:
Some number $x$ lies in some set. and we choose some $\epsilon$ in this set and we say "the $\epsilon$-neighborhood of $x$ is the set which lies with $|\epsilon|$-radius around $x$". Am I okay what this?
So as for my problem: $A:= \{2,3,4\}$, right? Then how can I choose a number from $\mathbb{R}$ and from $\mathbb{C}$ which lies in my $x$-set so that $A$ will be a neighborhood?
What is difference between complex and reals in terms of neighborhood?