## Set

belong to

$x \in A$

x \in A

\in comes from "x is in A".

belong to 2

$A \ni x$

A \ni x

Reversing \in to \ni changes the direction of the symbol.

not belong to

$x \notin A$

x \notin A

\notin comes from "x is not in A".

subset

$A \subset B$

A \subset B

It shows A is a subset of B.

subset 2

$A \subseteq B$

A \subseteq B

\subseteq means "subset or equal".

subset 3

$A \subseteqq B$

A \subseteqq B

If you repeat q, the two lines are shown on the bottom.

superset

$A \supset B$

A \supset B

This shows A is a superset of B.

superset 2

$A \supseteq B$

A \supseteq B

\supseteq means "superset or equal".

superset 3

$A \supseteqq B$

A \supseteqq B

If you repeat q, the two lines are shown on the bottom.

not subset

$A \not \subset B$

A \not \subset B

If you combine \not and \subset, the slashed line will be added.

proper subset

$A \subsetneqq B$

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.

intersection

$A \cap B$

A \cap B
union

$A \cup B$

A \cup B
empty set

$\varnothing$

\varnothing

The symbol is for an empty set, which comes from "nothing". It is similar to but different from the Greek letter phi.

empty set 2

$\emptyset$

\emptyset

The symbol is for an empty set, which comes from "empty set". It is similar to but different from the Greek letter phi.

complement set

$A^c$

A^c

"c" comes from "complement set".

complement set 2

$\overline{ A }$

\overline{ A }

You can also draw a line over the set to represent the complementary set.

complement set sample

$\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }$

\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }

This is De Morgan's Law.

complement set sample 2

$\begin{eqnarray} \left( \bigcup_{\lambda\in\Lambda}A_{\lambda} \right)^c =\bigcap_{\lambda\in\Lambda}A_{\lambda}^c \end{eqnarray}$

\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.

set difference

$A \setminus B$

A \setminus B

\setminus means a difference set. It is similar to backslash, but differs that \setminus contains a space before and after it.

set difference sample

$A \setminus B = A \cap B^c = \{ x \in A \mid x \notin B \}$

A \setminus B
= A \cap B^c
= \{ x \in A \mid x \notin B \}

This is the definition of a difference set.

symmetric difference

$A \triangle B$

A \triangle B

The symmetric difference is represented by a triangle.

symmetric difference sample

$A \triangle B = (A \setminus B) \cup (B \setminus A)$

A \triangle B
= (A \setminus B) \cup (B \setminus A)

This is the definition of the symmetric difference.

all natural numbers

$\mathbb{ N }$

\mathbb{ N }

This is the blackboard bold.

all integers

$\mathbb{ Z }$

\mathbb{ Z }
all rational numbers

$\mathbb{ Q }$

\mathbb{ Q }
all real numbers

$\mathbb{ R }$

\mathbb{ R }
all complex numbers

$\mathbb{ C }$

\mathbb{ C }
all quaternions

$\mathbb{ H }$

\mathbb{ H }
supremum

$\sup A$

\sup A
infimum

$\inf A$

\inf A
aleph number

$\aleph$

\aleph

It is used to express the cardinality of an infinite set.

Formula
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