What is the meaning of "Then S ∖m \\eq ∅; otherwise S is a subset of a finite set; a contradiction"?

Question

What is the meaning of "Then S ∖m
`\\eq` ∅; otherwise S is a subset of a finite set; a contradiction"?

Answer 1

It means that if S minus m (S \ m) is an empty set, then S is a subset of a finite set, which leads to a contradiction. Therefore, S minus m must not be an empty set.