Difference between backslash and minus on domain, range

Question

When declaring domain or range, is "$R\setminus\{0\}$" any different than "$R-\{0\}$"?

Answer 1

In principle, no. This is a matter of preference.

In practice, sometimes yes. $A-B$ sometimes denotes $\{a-b\mid a\in A, b\in B\}$ when $A$ and $B$ are subset of some set where subtraction is well-defined (e.g. sets of reals).

The rule of thumb is that when in doubt, define your notation explicitly. If you are the reader, ask to be sure.

Answer 2

The notation "$R \setminus {0}$" is usually used when dealing with sets (TeX command: "\setminus").

But also the minus sign is sometimes used and accepted.

Refer also to:

• Set Difference