Set
$x \in A$
x \in A
\in comes from "x is in A".
$A \ni x$
A \ni x
Reversing \in to \ni changes the direction of the symbol.
$x \notin A$
x \notin A
\notin comes from "x is not in A".
$A \subset B$
A \subset B
It shows A is a subset of B.
$A \subseteq B$
A \subseteq B
\subseteq means "subset or equal".
$A \subseteqq B$
A \subseteqq B
If you repeat q, the two lines are shown on the bottom.
$A \supset B$
A \supset B
This shows A is a superset of B.
$A \supseteq B$
A \supseteq B
\supseteq means "superset or equal".
$A \supseteqq B$
A \supseteqq B
If you repeat q, the two lines are shown on the bottom.
$A \not \subset B$
A \not \subset B
If you combine \not and \subset, the slashed line will be added.
$A \subsetneqq B$
A \subsetneqq B
This shows A is a proper subset of B. If you use \supsetneqq, that shows A is a proper superset of B.
$A \cap B$
A \cap B
$A \cup B$
A \cup B
$\varnothing$
\varnothing
The symbol is for an empty set, which comes from "nothing". It is similar to but different from the Greek letter phi.
$\emptyset$
\emptyset
The symbol is for an empty set, which comes from "empty set". It is similar to but different from the Greek letter phi.
$A^c$
A^c
"c" comes from "complement set".
$\overline{ A }$
\overline{ A }
You can also draw a line over the set to represent the complementary set.
$\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }$
\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }
This is De Morgan's Law.
$\begin{eqnarray} \left( \bigcup_{\lambda\in\Lambda}A_{\lambda} \right)^c =\bigcap_{\lambda\in\Lambda}A_{\lambda}^c \end{eqnarray}$
\begin{eqnarray} \left( \bigcup_{\lambda\in\Lambda}A_{\lambda} \right)^c =\bigcap_{\lambda\in\Lambda}A_{\lambda}^c \end{eqnarray}
This is De Morgan's Law too.
$A \setminus B$
A \setminus B
\setminus means a difference set. It is similar to backslash, but differs that \setminus contains a space before and after it.
$A \setminus B = A \cap B^c = \{ x \in A \mid x \notin B \}$
A \setminus B = A \cap B^c = \{ x \in A \mid x \notin B \}
This is the definition of a difference set.
$A \triangle B$
A \triangle B
The symmetric difference is represented by a triangle.
$A \triangle B = (A \setminus B) \cup (B \setminus A)$
A \triangle B = (A \setminus B) \cup (B \setminus A)
This is the definition of the symmetric difference.
$\mathbb{ N }$
\mathbb{ N }
This is the blackboard bold.
$\mathbb{ Z }$
\mathbb{ Z }
$\mathbb{ Q }$
\mathbb{ Q }
$\mathbb{ R }$
\mathbb{ R }
$\mathbb{ C }$
\mathbb{ C }
$\mathbb{ H }$
\mathbb{ H }
$\sup A$
\sup A
$\inf A$
\inf A
$\aleph$
\aleph
It is used to express the cardinality of an infinite set.