Meaning of the backslash operator on sets
I am self-studying analysis and ran across this:
$\mathbb R \setminus \mathbb N$ is an open subset of $\mathbb R$
My best guess for interpretation was this:
the set $\mathbb R \setminus \mathbb N$ is an open subset of $\mathbb R$.
which doesn't mean much to me. Can anyone clear this up a bit? I know that the 'divided by' symbol is usually a slash in the opposite direction. And I am unsure how I would divide the reals by the naturals anyway.
$\endgroup$2 Answers
$\begingroup$It’s set theoretic complement and in this case it denotes the set of all reals which are not natural: $$ℝ \setminus ℕ = \{x ∈ ℝ;~x \notin ℕ\}$$
$\endgroup$ 3 $\begingroup$The backward slash is kind of the set theory equivalent of subtracting, i.e.,
$$A\setminus B=\{a\in{A}\mid a\notin{B}\}\;.$$
$\endgroup$ 5
