Complement of the set B in A is indicated as A\B (see$_1$). Is there any significance for this slanted version of the symbol? Who first introduced it?

Source: $_1$ Fundamental Concepts of Abstract Algebra by Gertrude Ehrlich.


2 Answers 2


See ISO 31-11 part of international standard ISO 31 (1992) that defines mathematical signs and symbols for use in physical sciences and technology :

$A \setminus B$ : difference between $A$ and $B$; $A$ minus $B$. The set of elements which belong to $A$ but not to $B$.

$A \setminus B = \{ x ∣ x ∈ A ∧ x ∉ B \}$

$A − B$ should not be used.

Originally was $A-B$; from Hausdorff (1927, 1937), Kuratowski (1933) and Bourbaki (1939-1957), to Halmos (1960) and Devlin (1979, 1993).


Originally a set difference was written $A - B$. But of course when $A,B$ are sets of numbers, that may also mean $\{a-b : a \in A , b \in B\}$. So it is confusing. To reduce confusion, one can see $A \sim B$ for this subtraction, or (most common nowadays) $A \setminus B$ as you note.

(I have no information on who first used it.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.