What ∩ means
Only what belongs to both sets counts. In A ∩ B, keep elements in both A and B; with no overlap, the result is the empty set.
Called cap, it started as a general operation sign in 1844, then Peano fixed it as intersection in 1888, paired with ∪.
Why does ∩ sometimes mean AND?
Shared membership works like AND. x ∈ A ∩ B means x ∈ A and x ∈ B; the large ⋂ extends this to every set, a form Peano introduced in 1908.
Don't confuse it with
2Combination ideas
2Shared elements of A and B.
A and B share nothing.
Questions people ask
1Why does ∩ render oddly?
It can. Pick a math font with U+2229 support.
How to type ∩
Windows (Word)
Alt+XType 2229, then Alt+X to get ∩.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “intersection”.
Linux
Ctrl+Shift+UType 2229, then Enter or Space.
HTML
∩CSS
\2229LaTeX
Write \cap, as in A \cap B.
Codes and encoding1 code points
HTML decimal
∩
HTML hex
∩
CSS content
content: "\2229";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%88%A9
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.