Symbols

Arithmetic symbols and definitions.

$A\subset B$ ("A sub B")

A is included in B or A is subset of B.
$\forall a\in A\Rightarrow a\in B$

$A\supset B$("A sup B")

A includes B or A is superset of B.
$\forall b\in B\Rightarrow b\in A$

$A⊊B$("A included in and not equal to B")

A is included in but not equal to B.
$A\subset B and A\ne B$

$A⊋B$("A includes but is not equal to B")

A includes B but is not equal to it
$A\supset B and A\ne B$

$A\cup B$ ("A cup B" or "A union B")

The union of A and B contains all elements of either A or B.
$A\cup B:=\left\{x|x\in A or B\right\}$

$A\cap B$ ("A cap B" or "A intersects B")

The intersection of A and B contains all elements that are common of A and B.
$A\cap B:=\left\{x|x\in A and B\right\}$

${\cup }_{i\in I}{X}_i$ (Union of all X_i for i in I)

The union of the sets X_i for all indeces of I contains all elements of any X_i.
${\cup }_{i\in I}{X}_i:=\left\{x|\exists i\in I\mathrm{,x}\in X_i\right\}$

${\cap }_{i\in I}{X}_i$ (Intersection of all X_i for i in I)

The intersection of the sets X_i contains that elements common of all X_i.
${\cap }_{i\in I}{X}_i:=\left\{x|\forall i\in I\mathrm{,x}\in X_i\right\}$

A ∖ B; A-B ("A minus B" or "A setminus B")

The differenz of two sets A and B contains all elements that lie in A and not in B.
$A\setminus B:=\left\{x\right|x\in A and x\notin B\}$

$A▵B$ ("A triangle B")

The symmetric differenz of two sets A and B contains all elements that lie in either A or B but not in A and B.
$A▵B:=\left\{x\right|x\in A\cup B\setminus A\cap B\}$

Element

Elements are denoted by small letters $\mathrm{(a,}\mathrm{b,}\mathrm{x,}\mathrm{y,}\mathrm{...)}$ and collected in sets

Set

Sets are denoted by capital letters $\mathrm{(A,}\mathrm{B,}\mathrm{X,}\mathrm{Y,}\mathrm{...)}$.