# Element character

Mathematical signs
arithmetic
Plus sign +
Minus sign - , ./.
Mark , ×
Divided sign : , ÷ , /
Plus minus sign ± ,
Comparison sign < , , = , , >
Root sign
Percent sign %
Analysis
Sum symbol Σ
Product mark Π
Difference sign , Nabla ,
Prime
Partial differential
Integral sign
Concatenation characters
Infinity symbol
geometry
Angle sign , , ,
Vertical , parallel ,
Triangle , square ,
Diameter sign
Set theory
Union , cut ,
Difference , complement ,
Element character
Subset , superset , , ,
Empty set
logic
Universal quantifier
Existential quantifier
Conjunction , disjunction ,
Negation sign ¬

The element character (∈) is a mathematical symbol used to indicate that an object is an element of a set . It goes back to Giuseppe Peano and was created through stylization from the Greek lowercase letter epsilon . A number of modifications exist for the element sign; it is often used in a crossed-out form (∉) or upside down (∋).

## history

The founder of set theory Georg Cantor did not yet use an abbreviation for the expression a is an element of b . The element sign goes back to the Italian mathematician Giuseppe Peano, who first used it in the form of a Greek lowercase letter ϵ (epsilon) in 1889 in a work on the Peano axioms written in Latin :

"Signum ϵ significat est . Ita a ϵ b legitur a est quoddam b "

“The sign ϵ means is . So a ϵ b is read as a is a b "

- Giuseppe Peano : Arithmetices principia nova methodo exposita , 1889, p. X

The epsilon ϵ, which Peano wrote from 1890 in the form ε , is the initial of the Greek word ἐστί (esti) with the meaning is . In the form ε and the verbalization that is common today , the element sign was used in 1907 by Ernst Zermelo in his work on Zermelo set theory . In its original form ϵ, the element symbol spread from 1910 onwards via the Principia Mathematica by Bertrand Russell and Alfred North Whitehead . In the course of time it was then stylized to ∈.

## use

If an object is an element of a set , this fact is noted ${\ displaystyle x}$${\ displaystyle M}$

${\ displaystyle x \ in M}$

and says "x is an element of M".

Occasionally it makes sense to reverse the order and then note it down

${\ displaystyle M \ ni x}$

and says "M contains as element x".

If there is no element of the set , one writes accordingly ${\ displaystyle x}$${\ displaystyle M}$

${\ displaystyle x \ notin M}$   or   .${\ displaystyle M \ not \ ni x}$

Formally, the element sign stands for a relation , the so-called element relation.

## Coding

### Element character

The element character can be found in the Unicode block mathematical operators and is coded as follows in computer systems.

Coding in Unicode , HTML and LaTeX
character Unicode designation HTML Latex
U+2208 element of Element of & # x2208; & # 8712; ? \in
U+2209 not an element of no element of & # x2209; & # 8713; & notin; \notin
U+220A small element of small element of & # x220A; & # 8714;
U+220B contains as member contains as an element & # x220B; & # 8715; ? \ni
U+220C does not contain as a member does not contain as an element & # x220C; & # 8716; \not\ni
U+220D small contains as member contains small as an element & # x220D; & # 8717;
U+27D2 element of opening upwards Element opened from the top & # x27D2; & # 10194;
U+2AD9 element of opening downwards Element opened from the bottom & # x2AD9; & # 10969;

### epsilon

The Greek lowercase letter epsilon is also occasionally used as an element character.

Coding in Unicode , HTML and LaTeX
character Unicode designation HTML Latex
ε U+03B5 greek small letter epsilon greek lowercase letter epsilon & # x03B5; & # 949; ε \varepsilon
ϵ U+03F5 greek lunate epsilon symbol greek crescent-shaped epsilon symbol & # x03F5; & # 1013; \epsilon
϶ U+03F6 greek reversed lunate epsilon symbol greek inverted crescent-shaped epsilon symbol & # x03F6; & # 1014;

### Modifications

The following modifications of the element symbol also exist.

Coding in Unicode and HTML
character Unicode designation HTML
U+22F2 element of with long horizontal stroke Element of with a long horizontal bar & # x22F2; & # 8946;
U+22F3 element of with vertical bar at end of horizontal stroke Element of with a vertical bar at the end of the horizontal bar & # x22F3; & # 8947;
U+22F4 small element of with vertical bar at end of horizontal stroke small element of with a vertical bar at the end of the horizontal line & # x22F4; & # 8948;
U+22F5 element of with dot above Element from with point above & # x22F5; & # 8949;
U+22F6 element of with overbar Element of with overline & # x22F6; & # 8950;
U+22F7 small element of with overbar small element of with overline & # x22F7; & # 8951;
U+22F8 element of with underbar Element of with underscore & # x22F8; & # 8952;
U+22F9 element of with two horizontal strokes Element of with two horizontal bars & # x22F9; & # 8953;
U+22FA contains with long horizontal stroke contains with a long horizontal line & # x22FA; & # 8954;
U+22FB contains with vertical bar at end of horizontal stroke includes with a vertical bar at the end of the horizontal bar & # x22FB; & # 8955;
U+22FC small contains with vertical bar at end of horizontal stroke small contains with a vertical bar at the end of the horizontal bar & # x22FC; & # 8956;
U+22FD contains with overbar contains with overline & # x22FD; & # 8957;
U+22FE small contains with overbar small contains with overline & # x22FE; & # 8958;