sometimes we use notation $S;x$ as an abbreviation for $S\cup \lbrace x\rbrace$.
(H.B. Enderton, Mathematical Introduction to Logic.)
but we also sometimes need delete a member from a set.
for example, in $\epsilon-\delta$ definition of limit, we have to consider a domain $(x-\delta,x+\delta)-\lbrace a\rbrace$ to decide $\lim_{x\to a}f(x)$.
so I think there might(should) be a simple notation for this kind of operation.
is there any notation for this kind of operation?