Follow arrow

⇒ ⇔ ⇐
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 following arrow is a double arrow pointing right, left or both sides. It is the mathematical notation for a logical conclusion .

use

The following arrow is the mathematical symbol for “it follows,” the logical conclusion . It represents a logical connection : the symbol is used when a correct conclusion is drawn from something right, a wrong conclusion from something wrong, or a right conclusion from something wrong. However, it must never be used to infer something wrong from something right.

x ist durch 4 teilbar ⇒ x ist durch 2 teilbar ⇒ x ist gerade

(here a transitive conclusion , it also follows directly x ist durch 4 teilbar ⇒ x ist gerade)

Of course you can rearrange the conclusions at any time (“follows from”), and then use ⇐ (next arrow on the left). In addition, one can use the arrow ⇔ for mutual conclusions ( equivalence relations ) and say "follows mutually" or "follows equivalently":

4 mal x ist 8 ⇔ 8 durch 4 ist x

Both statements describe the same facts, only formulated differently: They are interchangeable.

If one statement does not follow from another, "does not follow from this" ⇏ is crossed out. Here, too, there is ⇎ "it does not follow equivalent" - but this does not make a statement as to whether the conclusion in one direction is not correct:

x ist durch 4 teilbar ⇎ x ist durch 2 teilbar

with the first example, because one cannot infer from x that x is divisible by 4, but only that it is divisible by 2: The statements “even” and “divisible by 2” are equivalent.

In the various sub-areas and for more precise statements, there are numerous more specific variations of this arrow symbolism.

Word processing and typesetting

The arrow can also be represented with =>( equal sign and greater than sign ), and is converted in some editors after input.

In Unicode , the mathematical arrows are located in the Unicode block arrows (arrows, 2190–21FF) at the code points:

designation	character	HEX code
RIGHTWARDS DOUBLE ARROW	⇒	0x21d2 U + 21D2
LEFTWARDS DOUBLE ARROW	⇐	0x21d0 U + 21D0
LEFT RIGHT DOUBLE ARROW	⇔	0x21d4 U + 21D4
RIGHTWARDS DOUBLE ARROW WITH STROKE	⇏	0x21d0 U + 21CF
LEFTWARDS DOUBLE ARROW WITH STROKE	⇍	0x21d2 U + 21CD
LEFT RIGHT DOUBLE ARROW WITH STROKE	⇎	0x21d4 U + 21CE

In addition, there are the same up and down arrows, which can be used in a flowchart-like sentence (in the same block), as well as in an extended form if this is necessary in the sentence (in the Unicode block Additional arrows-A 27F0-27FF)

In TeX they are called \Leftarrow and \Rightarrowand \Leftrightarrow(with a capital in explicit distinction for easy arrow) or \nLeftarrow, \nRightarrow, \nLeftrightarrow(preceded by small ' n' for negation set). There are also several variants here:

syntax Result \circlearrowleft \circlearrowright ${\displaystyle \circlearrowleft \circlearrowright }$ \curvearrowleft \curvearrowright ${\displaystyle \curvearrowleft \curvearrowright }$ \downarrow \uparrow ${\displaystyle \downarrow \uparrow }$ \downdownarrows \upuparrows ${\displaystyle \downdownarrows \upuparrows }$ \Downarrow \Uparrow ${\displaystyle \Downarrow \Uparrow }$ \hookleftarrow \hookrightarrow ${\displaystyle \hookleftarrow \;\hookrightarrow }$ \leftarrow \rightarrow ${\displaystyle \leftarrow \;\rightarrow }$ \Leftarrow \Rightarrow ${\displaystyle \Leftarrow \;\Rightarrow }$ \leftarrowtail \rightarrowtail ${\displaystyle \leftarrowtail \rightarrowtail }$ \leftharpoondown \rightharpoondown ${\displaystyle \leftharpoondown \;\rightharpoondown }$ \leftharpoonup \rightharpoonup ${\displaystyle \leftharpoonup \;\rightharpoonup }$ \leftleftarrows \rightrightarrows ${\displaystyle \leftleftarrows \rightrightarrows }$ \leftrightarrow \Leftrightarrow ${\displaystyle \leftrightarrow \Leftrightarrow }$ \leftrightarrows \rightleftarrows ${\displaystyle \leftrightarrows \rightleftarrows }$ \leftrightharpoons \rightleftharpoons ${\displaystyle \leftrightharpoons \rightleftharpoons }$

syntax Result \leftrightsquigarrow \rightsquigarrow ${\displaystyle \leftrightsquigarrow \rightsquigarrow }$ \Lleftarrow \Rrightarrow ${\displaystyle \Lleftarrow \Rrightarrow }$ \longleftarrow \longrightarrow ${\displaystyle \longleftarrow \longrightarrow }$ \Longleftarrow \Longrightarrow ${\displaystyle \Longleftarrow \Longrightarrow }$ \longleftrightarrow ${\displaystyle \longleftrightarrow }$ \Longleftrightarrow ${\displaystyle \Longleftrightarrow }$ \longmapsto \mapsto ${\displaystyle \longmapsto \mapsto }$ \looparrowleft \looparrowright ${\displaystyle \looparrowleft \;\looparrowright }$ \Lsh \Rsh ${\displaystyle \Lsh \;\Rsh }$ \multimap ${\displaystyle \multimap }$ \nearrow \nwarrow \searrow \swarrow ${\displaystyle \nearrow \nwarrow \searrow \swarrow }$ \nLeftarrow \nRightarrow ${\displaystyle \nLeftarrow \;\nRightarrow }$ \nleftrightarrow \nLeftrightarrow ${\displaystyle \nleftrightarrow \nLeftrightarrow }$ \restriction ${\displaystyle \upharpoonright }$ \twoheadleftarrow \twoheadrightarrow ${\displaystyle \twoheadleftarrow \;\twoheadrightarrow }$ \updownarrow \Updownarrow ${\displaystyle \updownarrow \;\Updownarrow }$

See also

• implication
• Arrow (symbol)
• Biconditional (⇔)

Individual evidence

1. ↑ List of mathematical symbols. mathe-online.at, accessed on March 3, 2012 .