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 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 "
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 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.
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 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.
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 3-642-01445-3 .
Individual evidence
- ↑ a b Oliver Deiser: Introduction to set theory . Springer, 2009, ISBN 978-3-642-01444-4 , 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 .