Example 0.3.7.

If \(A = \{1,2,3\}\text{,}\) then we can describe the set we get by adding the number 4 as \(A \cup \{4\}\text{.}\) If we want to express the set we get by removing the number 2 from \(A\) we can do so by writing \(A \setminus \{2\}\text{.}\)

Careful though. If you add an element to the set, you get a new set! So you would have \(B = A \cup \{4\}\) and then correctly say that \(B\) contains 4, but \(A\) does not.