Symbols:Set Theory/Variants

Variant Symbols of Set Theory

Set Difference

$-$

A variant notation for the difference between two sets $S$ and $T$ is $S - T$.

The $\LaTeX$ code for \(S - T\) is S - T .

Symmetric Difference

There is no standard symbol for symmetric difference. The one used here, and in general on $\mathsf{Pr} \infty \mathsf{fWiki}$:

$S \symdif T$

is the one used in 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics.

The following are often found for $S \symdif T$:

$S * T$

$S \oplus T$

$S + T$

$S \mathop \triangle T$

According to 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: symmetric difference:

$S \mathop \Theta T$

$S \mathop \triangledown T$

are also variants for denoting this concept.

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.): symmetric difference recognizes a further variant:

$S \mathop \nabla T$

$\map n S$ Notation

$\map n S$

The cardinality of a set $S$ can be denoted:

$\map n S$

Its $\LaTeX$ code is \map n S .

$\#$ Notation

$\# S$

The cardinality of a set $S$ can be denoted:

$\# S$

Its $\LaTeX$ code is \# S .

Overline

$\overline S$

The cardinality of a set $S$ can be denoted:

$\overline S$

Its $\LaTeX$ code is \overline S .