Set | Easy Copy Mathjax

belong to

$x \in A$

x \in A

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\in comes from "x is in A".

belong to 2

$A \ni x$

A \ni x

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

not belong to

$x \notin A$

x \notin A

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

subset

$A \subset B$

A \subset B

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It shows A is a subset of B.

subset 2

$A \subseteq B$

A \subseteq B

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\subseteq means "subset or equal".

subset 3

$A \subseteqq B$

A \subseteqq B

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

superset

$A \supset B$

A \supset B

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This shows A is a superset of B.

superset 2

$A \supseteq B$

A \supseteq B

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\supseteq means "superset or equal".

superset 3

$A \supseteqq B$

A \supseteqq B

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

not subset

$A \not \subset B$

A \not \subset B

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

proper subset

$A \subsetneqq B$

A \subsetneqq B

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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

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union

$A \cup B$

A \cup B

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empty set

$\varnothing$

\varnothing

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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

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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

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"c" comes from "complement set".

complement set 2

$\overline{ A }$

\overline{ A }

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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 }

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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}

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This is De Morgan's Law too.

set difference

$A \setminus B$

A \setminus B

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\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 \}

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This is the definition of a difference set.

symmetric difference

$A \triangle B$

A \triangle B

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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)

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This is the definition of the symmetric difference.

all natural numbers

$\mathbb{ N }$

\mathbb{ N }

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This is the blackboard bold.

all integers

$\mathbb{ Z }$

\mathbb{ Z }

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all rational numbers

$\mathbb{ Q }$

\mathbb{ Q }

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all real numbers

$\mathbb{ R }$

\mathbb{ R }

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all complex numbers

$\mathbb{ C }$

\mathbb{ C }

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all quaternions

$\mathbb{ H }$

\mathbb{ H }

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supremum

$\sup A$

\sup A

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infimum

$\inf A$

\inf A

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aleph number

$\aleph$

\aleph

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