Why is the notation $A\setminus B$ preferred over $A-B$?

Question

Let $A$ and $B$ be sets, why is the notation $A\setminus B$ preferred over $A-B$ for set differences?

IMO there is no "deep reason" why it is so... Authoritative textbook of 20th Century (Hausdorff, Bourbaki) used the "$-$" sign. — Mauro ALLEGRANZA, Sep 14 '20 at 13:01

score 7 · Accepted Answer · edited Sep 14 '20 at 13:02

7

In some contexts $A-B$ might refer to things like the Minkowski difference of two subsets of a vector space, like $A+B$ almost always refers to the sum $\{a+b\mid a\in A, b\in B\}$.

The notation $A\setminus B$ is less likely to collide with other common interpretations of $A-B$.

edited Sep 14 '20 at 13:02

J. W. Tanner

60,406

answered Sep 14 '20 at 12:57

Christoph

24,912

score 3 · Answer 2 · answered Sep 14 '20 at 12:57

3

Because $A-B$ is ambiguous and could mean $\{a-b:a\in A, b\in B\}$.

answered Sep 14 '20 at 12:57

RobPratt

45,619

Why is the notation $A\setminus B$ preferred over $A-B$?

2 Answers2