# What does the subset with slash symbol mean?

What does the following mean:

$\nsubseteq$

I cant find any definition for it?

Previous editor's note: I replaced a linked image with the $\nsubseteq$ symbol to make the question self-contained. I am pointing this out here to avoid comments/questions such as, "You don't know what it means but you know how to write it in $\mathrm\TeX$?"

• "is not a subset of" – user137731 Sep 20 '16 at 0:40
• Is not a subset of – mattapow Sep 20 '16 at 0:40

Quite simply, $\not\subseteq$ means "not subset of." Hence, $A\not\subseteq B$ means that $A$ is not a subset of $B$.

All the more to make this clear, that symbol is easily typeset with \not\subseteq.

Is not a subset of. If $A \nsubseteq B$, it means that $A$ is not a subset of $B$.

• Is there any distinction between $\not\subseteq$ and $\not\subset$? – Robert Soupe Sep 20 '16 at 6:23
• @RobertSoupe I'm not sure, but if I were to guess I would say that that would mean not a strict subset of, i.e. that $A\not\subseteq B$ disallows $A=B$ but $A\not\subset B$ allows it. – Carl Schildkraut Sep 20 '16 at 13:56

If A ⊈ B, then no member of A is a member of B.

The symbol '⊈' represent the negation of the relation of improper inclusion, '⊆'. A ⊆ B if and only if all member of A is a member of B or if A = B.

Must be distinguished from the negation of the proper inclusion '⊂'. 'A ⊂ B' says that all member of A are members of B, but is not the case that A = B.

Thereby, for example, A ⊆ A, but is not the case that A ⊂ A.