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  
Follow arrow  ⇒ , ⇔ , ⇐ 
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 crossedout 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 "
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
and says "x is an element of M".
Occasionally it makes sense to reverse the order and then note it down
and says "M contains as element x".
If there is no element of the set , one writes accordingly
 or .
Formally, the element sign stands for a relation , the socalled 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.
character  Unicode  designation  HTML  Latex  

position  designation  hexadecimal  decimal  named  
∈ 
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.
character  Unicode  designation  HTML  Latex  

position  designation  hexadecimal  decimal  named  
ε 
U+03B5

greek small letter epsilon  greek lowercase letter epsilon  & # x03B5;  & # 949;  ε 
\varepsilon

ϵ 
U+03F5

greek lunate epsilon symbol  greek crescentshaped epsilon symbol  & # x03F5;  & # 1013; 
\epsilon


϶ 
U+03F6

greek reversed lunate epsilon symbol  greek inverted crescentshaped epsilon symbol  & # x03F6;  & # 1014; 
Modifications
The following modifications of the element symbol also exist.
character  Unicode  designation  HTML  

position  designation  hexadecimal  decimal  
⋲ 
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; 
See also
literature
 Oliver Deiser: Introduction to set theory . Springer, 2009, ISBN 3642014453 .
Individual evidence
 ↑ ^{a } ^{b} Oliver Deiser: Introduction to set theory . Springer, 2009, ISBN 9783642014444 , pp. 21 .
 ↑ See https://archive.org/details/arithmeticespri00peangoog for a link to the original work. File: First usage of the symbol ∈.png contains a picture of the corresponding text passage.
 ^ Giuseppe Peano: Démonstration de l'intégrabilité des equations différentielles ordinaires . In: Mathematical Annals . tape 37 , 1890, p. 183 .
 ↑ Ernst Zermelo: Investigations on the basics of set theory . In: Mathematical Annals . tape 65 , 1908, pp. 262 .
 ^ Bertrand Russell, Alfred North Whitehead: Principia Mathematica . Volume 1. Cambridge University Press, 1910, pp. 26 .