Difference between revisions of "List of mathematical symbols"
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!width="5%"| Symbol | !width="5%"| Symbol | ||
!width="9%"| Usage | !width="9%"| Usage | ||
− | !width=" | + | !width="48%"| Interpretation |
− | !width=" | + | !width="12%"| Article |
!width="10%"| LaTeX | !width="10%"| LaTeX | ||
!width="8%"| HTML | !width="8%"| HTML | ||
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|style="text-align:center"| <math>\tilde{a}</math> | |style="text-align:center"| <math>\tilde{a}</math> | ||
| Reciprocal of <math>a</math>: <math>1/a</math> resp. <math>a^{-1}</math> for <math>a \ne 0</math> (read as "turn") | | Reciprocal of <math>a</math>: <math>1/a</math> resp. <math>a^{-1}</math> for <math>a \ne 0</math> (read as "turn") | ||
− | | | + | | [[w:Multiplicative inverse|<span class="wikipedia">Reciprocal</span>]] |
| <code>\widetilde{}</code> | | <code>\widetilde{}</code> | ||
| | | | ||
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|style="text-align:center"| <math>\acute{a}</math> | |style="text-align:center"| <math>\acute{a}</math> | ||
| Increment of <math>a</math>: <math>a - 1</math> (read as "dec") | | Increment of <math>a</math>: <math>a - 1</math> (read as "dec") | ||
− | | | + | | [[w:Increment and decrement operators|<span class="wikipedia">Increment</span>]] |
| <code>\acute{}</code> | | <code>\acute{}</code> | ||
| | | | ||
| <code>U+00B4</code> | | <code>U+00B4</code> | ||
|- | |- | ||
− | |style="text-align:center"| <math>\grave{}</math> | + | |style="text-align:center"| <math>\overset{\scriptsize{\grave{}}}{}</math> |
− | |style="text-align:center"| <math>\grave{a}</math> | + | |style="text-align:center"| <math>\overset{\scriptsize{\grave{}}}{a}</math> |
| Decrement of <math>a</math>: <math>a + 1</math> (read as "inc") | | Decrement of <math>a</math>: <math>a + 1</math> (read as "inc") | ||
− | | | + | | [[w:Increment and decrement operators|<span class="wikipedia">Decrement</span>]] |
| <code>\grave{}</code> | | <code>\grave{}</code> | ||
| | | | ||
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|style="text-align:center"| <math>\hat{a}</math> | |style="text-align:center"| <math>\hat{a}</math> | ||
| Double of <math>a</math>: <math>2a</math> (read as "hat") | | Double of <math>a</math>: <math>2a</math> (read as "hat") | ||
− | | | + | | [[w:Double#Mathematics_and_computing|<span class="wikipedia">Double</span>]] |
| <code>\widehat{}</code> | | <code>\widehat{}</code> | ||
| | | | ||
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|style="text-align:center"| <math>\check{a}</math> | |style="text-align:center"| <math>\check{a}</math> | ||
| Half of <math>a</math>: <math>a/2</math> (read as "half") | | Half of <math>a</math>: <math>a/2</math> (read as "half") | ||
− | | | + | | [[w:One_half#Mathematics|<span class="wikipedia">One half</span>]] |
| <code>\widecheck{}</code> | | <code>\widecheck{}</code> | ||
| | | | ||
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|style="text-align:center"| <math>a\text{-}</math> | |style="text-align:center"| <math>a\text{-}</math> | ||
| <math>a</math> negated: <math>a\text{-}</math> (read as "neg") | | <math>a</math> negated: <math>a\text{-}</math> (read as "neg") | ||
− | | | + | | [[w:Plus_and_minus_signs#Minus_sign|<span class="wikipedia">Minus sign</span>]] |
| <code>\text{-}</code> | | <code>\text{-}</code> | ||
| | | | ||
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|style="text-align:center"| <math>z = a + \underline{b}</math> | |style="text-align:center"| <math>z = a + \underline{b}</math> | ||
| Complex part of <math>z</math>: <math>\underline{1}b</math> with imaginary unit <math>\underline{1}</math> (read as "comp") | | Complex part of <math>z</math>: <math>\underline{1}b</math> with imaginary unit <math>\underline{1}</math> (read as "comp") | ||
− | | | + | | [[w:Imaginary_unit#Imaginary_integers_and_imaginary_numbers|<span class="wikipedia">Imaginary unit</span>]] |
| <code>\underline{}</code> | | <code>\underline{}</code> | ||
| | | | ||
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|style="text-align:center"| <math>{}^{\nu} A</math> | |style="text-align:center"| <math>{}^{\nu} A</math> | ||
| greatest finite number: intersection of the complex or real set <math>A</math> for <math>{}^{\nu}\mathbb{C} := [-\nu, \; \nu] + \underline{1}[-\nu, \nu]</math> | | greatest finite number: intersection of the complex or real set <math>A</math> for <math>{}^{\nu}\mathbb{C} := [-\nu, \; \nu] + \underline{1}[-\nu, \nu]</math> | ||
− | | | + | | [[w:Finite set|<span class="wikipedia">Finite number</span>]] |
| <code>\nu</code> | | <code>\nu</code> | ||
| <code>&nu;</code> | | <code>&nu;</code> | ||
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|style="text-align:center"| <math>{}^{\omega} A</math> | |style="text-align:center"| <math>{}^{\omega} A</math> | ||
| greatest mid-finite number: intersection of the complex or real set <math>A</math> for <math>{}^{\omega}\mathbb{C} := [-\omega, \omega] + \underline{1}[-\omega, \omega]</math> | | greatest mid-finite number: intersection of the complex or real set <math>A</math> for <math>{}^{\omega}\mathbb{C} := [-\omega, \omega] + \underline{1}[-\omega, \omega]</math> | ||
− | | | + | | [[w:Transfinite number|<span class="wikipedia">Infinite number</span>]] |
| <code>\omega</code> | | <code>\omega</code> | ||
| <code>&omega;</code> | | <code>&omega;</code> | ||
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|style="text-align:center"| <math>\iota = \min \mathbb{R}_{>0}</math> | |style="text-align:center"| <math>\iota = \min \mathbb{R}_{>0}</math> | ||
| smallest positive real number | | smallest positive real number | ||
− | | | + | | [[w:Positive real numbers|<span class="wikipedia">Positive number</span>]] |
| <code>\iota</code> | | <code>\iota</code> | ||
| <code>&iota;</code> | | <code>&iota;</code> | ||
| <code>U+03B9</code> | | <code>U+03B9</code> | ||
+ | |- | ||
+ | |style="text-align:center"| <math>{}^n</math> | ||
+ | |style="text-align:center"| <math>{}^n a = a^{(n)}</math> | ||
+ | | <math>n</math>-th derivative of <math>a</math> (read as "n of a") | ||
+ | | [[w:Notation for differentiation|<span class="wikipedia">Derivative</span>]] | ||
+ | | <code>{}^n</code> | ||
+ | | | ||
+ | | | ||
|- | |- | ||
|style="text-align:center"| <math>{}_b</math> | |style="text-align:center"| <math>{}_b</math> | ||
|style="text-align:center"| <math>{}_b a = \log_b a</math> | |style="text-align:center"| <math>{}_b a = \log_b a</math> | ||
| Logarithm to base <math>b</math> for <math>a \in \mathbb{C} \setminus \mathbb{R}_{\le 0}</math> (read as "b log a") | | Logarithm to base <math>b</math> for <math>a \in \mathbb{C} \setminus \mathbb{R}_{\le 0}</math> (read as "b log a") | ||
− | | | + | | [[w:Logarithm|<span class="wikipedia">Logarithm</span>]] |
| <code>{}_b</code> | | <code>{}_b</code> | ||
| | | | ||
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|style="text-align:center"| <math>{}_1 x = x/||x||</math> | |style="text-align:center"| <math>{}_1 x = x/||x||</math> | ||
| Unit vector to <math>x \ne 0</math> | | Unit vector to <math>x \ne 0</math> | ||
− | | | + | | [[w:Unit vector|<span class="wikipedia">Unit vector</span>]] |
| <code>{}_1</code> | | <code>{}_1</code> | ||
| | | | ||
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| <code>&infin;</code> | | <code>&infin;</code> | ||
| <code>U+221E</code> | | <code>U+221E</code> | ||
+ | |- | ||
+ | |style="text-align:center"| <math>{}^{\pm}</math> | ||
+ | |style="text-align:center"| <math>{}^{\pm}A = A \cup \{\pm\infty\}</math> | ||
+ | | Extended complex (real) set <math>A \subseteq \mathbb{K}</math> | ||
+ | | [[w:Extended_real_number_line|<span class="wikipedia">Extended real number line</span>]] | ||
+ | | <code>\pm</code> | ||
+ | | <code>&plusmn;</code> | ||
+ | | <code>U+00B1</code> | ||
|- | |- | ||
|style="text-align:center"| <math>\mathbb M</math> | |style="text-align:center"| <math>\mathbb M</math> | ||
|style="text-align:center"| <math>{\mathbb{M}}_{\mathbb{R}} = {}^{\omega}{\mathbb{R}} \setminus {}^{\nu}{\mathbb{R}}</math> | |style="text-align:center"| <math>{\mathbb{M}}_{\mathbb{R}} = {}^{\omega}{\mathbb{R}} \setminus {}^{\nu}{\mathbb{R}}</math> | ||
| mid-finite numbers: <math>{\mathbb{M}}_{\mathbb{C}} := {\mathbb{M}}_{\mathbb{R}} + \underline{\mathbb{M}}_{\mathbb{R}}</math> | | mid-finite numbers: <math>{\mathbb{M}}_{\mathbb{C}} := {\mathbb{M}}_{\mathbb{R}} + \underline{\mathbb{M}}_{\mathbb{R}}</math> | ||
− | | | + | | [[w:Infinite set|<span class="wikipedia">Infinite set</span>]] |
| <code>\mathbb{M}</code> | | <code>\mathbb{M}</code> | ||
| <code>&Mopf;</code> | | <code>&Mopf;</code> | ||
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|style="text-align:center"| <math>\dot{A}</math> | |style="text-align:center"| <math>\dot{A}</math> | ||
|point-symmetric set <math>A</math> | |point-symmetric set <math>A</math> | ||
− | | | + | | [[w:Point_reflection#Point_reflections_in_mathematics|<span class="wikipedia">Point symmetry</span>]] |
| <code>\dot</code> | | <code>\dot</code> | ||
| <code>˙</code> | | <code>˙</code> | ||
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|style="text-align:center"| <math>A^{\ll}</math> | |style="text-align:center"| <math>A^{\ll}</math> | ||
|Set <math>A</math> without boundary <math>\partial A</math> given by min <math>\{d(x, y) : x \in A°, y \in A^{\prime}\} = \tilde{\nu}</math> | |Set <math>A</math> without boundary <math>\partial A</math> given by min <math>\{d(x, y) : x \in A°, y \in A^{\prime}\} = \tilde{\nu}</math> | ||
− | | | + | | [[w:Boundary (topology)|<span class="wikipedia">Boundary</span>]] |
| <code>{}^{\ll}</code> | | <code>{}^{\ll}</code> | ||
| <code>≪</code> | | <code>≪</code> | ||
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|style="text-align:center"| <math>A'</math> | |style="text-align:center"| <math>A'</math> | ||
|Complement of the set <math>A</math> | |Complement of the set <math>A</math> | ||
− | |[[w:Complement (set theory)|<span class="wikipedia">Complement | + | | [[w:Complement (set theory)|<span class="wikipedia">Complement</span>]] |
− | | | + | | <code>\prime</code> |
| | | | ||
| <code>U+0027</code> | | <code>U+0027</code> | ||
+ | |- | ||
+ | |style="text-align:center"| <math>\complement</math> | ||
+ | |style="text-align:center"| <math>\complement_1^n\ a_m</math> | ||
+ | |Concatenation of <math>a_m</math> to <math>a_1, ..., a_n</math> | ||
+ | | [[w:Concatenation|<span class="wikipedia">Concatenation operator</span>]] | ||
+ | | <code>\complement</code> | ||
+ | | <code>∁</code> | ||
+ | | <code>U+2201</code> | ||
|- | |- | ||
|style="text-align:center"| <math>\leftharpoonup</math> | |style="text-align:center"| <math>\leftharpoonup</math> | ||
|style="text-align:center"| <math>\overset{\leftharpoonup}{a}</math> | |style="text-align:center"| <math>\overset{\leftharpoonup}{a}</math> | ||
| Predecessor of <math>a</math> (read as "pre") | | Predecessor of <math>a</math> (read as "pre") | ||
− | | | + | | [[w:Predecessor problem|<span class="wikipedia">Predecessor</span>]] |
| <code>\leftharpoonup</code> | | <code>\leftharpoonup</code> | ||
| | | | ||
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|style="text-align:center"| <math>\overset{\rightharpoonup}{a}</math> | |style="text-align:center"| <math>\overset{\rightharpoonup}{a}</math> | ||
| Successor of <math>a</math> (read as "post") | | Successor of <math>a</math> (read as "post") | ||
− | | | + | | [[w:Glossary_of_graph_theory#successor|<span class="wikipedia">Successor</span>]] |
| <code>\rightharpoonup</code> | | <code>\rightharpoonup</code> | ||
| | | | ||
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|style="text-align:center"| <math>a{\upharpoonleft}_n</math> | |style="text-align:center"| <math>a{\upharpoonleft}_n</math> | ||
| <math>n</math>-fold repetition of <math>a</math> in the form <math>(a, ... , a)^T</math> (read as "rep") | | <math>n</math>-fold repetition of <math>a</math> in the form <math>(a, ... , a)^T</math> (read as "rep") | ||
− | | | + | | [[w:Repetition|<span class="wikipedia">Repetition</span>]] |
| <code>\upharpoonleft</code> | | <code>\upharpoonleft</code> | ||
| | | | ||
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|style="text-align:center"| <math>a{\upharpoonright}_n</math> | |style="text-align:center"| <math>a{\upharpoonright}_n</math> | ||
| Projection of <math>(a_1, ... , a_n)^T</math> onto the <math>k</math>-th entry <math>a_k</math> (read as "proj") | | Projection of <math>(a_1, ... , a_n)^T</math> onto the <math>k</math>-th entry <math>a_k</math> (read as "proj") | ||
− | | | + | | [[w:Projection (set theory)|<span class="wikipedia">Projection</span>]] |
| <code>\upharpoonright</code> | | <code>\upharpoonright</code> | ||
| | | | ||
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|style="text-align:center"| <math>\downarrow {x}</math> | |style="text-align:center"| <math>\downarrow {x}</math> | ||
| Differential of <math>x</math> (read as "down") | | Differential of <math>x</math> (read as "down") | ||
− | | | + | | [[w:Differential (mathematics)|<span class="wikipedia">Differential</span>]] |
| <code>\downarrow</code> | | <code>\downarrow</code> | ||
| <code>&darr;</code> | | <code>&darr;</code> | ||
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|style="text-align:center"| <math>\uparrow f(x)</math> | |style="text-align:center"| <math>\uparrow f(x)</math> | ||
| Integral of <math>f(x)</math> (read as "up") | | Integral of <math>f(x)</math> (read as "up") | ||
− | | | + | | [[w:Integral#Terminology_and_notation|<span class="wikipedia">Integral</span>]] |
| <code>\uparrow</code> | | <code>\uparrow</code> | ||
| <code>&uarr;</code> | | <code>&uarr;</code> | ||
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| | | | ||
|End of proof | |End of proof | ||
− | | | + | | [[w:Mathematical_proof#Ending_a_proof|<span class="wikipedia">Proof</span>]] |
| <code>\Box</code> | | <code>\Box</code> | ||
| | | | ||
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| | | | ||
|End of definition | |End of definition | ||
− | | | + | | [[w:Definition#In_logic,_mathematics_and_computing|<span class="wikipedia">Definition</span>]] |
| <code>\triangle</code> | | <code>\triangle</code> | ||
| <code>&Delta;</code> | | <code>&Delta;</code> |
Latest revision as of 02:01, 16 September 2024
The following mathematical symbols are used differently from Wikipedia:
Symbol | Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|
[math]\displaystyle{ \widetilde{} }[/math] | [math]\displaystyle{ \tilde{a} }[/math] | Reciprocal of [math]\displaystyle{ a }[/math]: [math]\displaystyle{ 1/a }[/math] resp. [math]\displaystyle{ a^{-1} }[/math] for [math]\displaystyle{ a \ne 0 }[/math] (read as "turn") | Reciprocal | \widetilde{}
|
U+007E
| |
[math]\displaystyle{ \acute{} }[/math] | [math]\displaystyle{ \acute{a} }[/math] | Increment of [math]\displaystyle{ a }[/math]: [math]\displaystyle{ a - 1 }[/math] (read as "dec") | Increment | \acute{}
|
U+00B4
| |
[math]\displaystyle{ \overset{\scriptsize{\grave{}}}{} }[/math] | [math]\displaystyle{ \overset{\scriptsize{\grave{}}}{a} }[/math] | Decrement of [math]\displaystyle{ a }[/math]: [math]\displaystyle{ a + 1 }[/math] (read as "inc") | Decrement | \grave{}
|
U+0060
| |
[math]\displaystyle{ \widehat{} }[/math] | [math]\displaystyle{ \hat{a} }[/math] | Double of [math]\displaystyle{ a }[/math]: [math]\displaystyle{ 2a }[/math] (read as "hat") | Double | \widehat{}
|
U+0302
| |
[math]\displaystyle{ \check{} }[/math] | [math]\displaystyle{ \check{a} }[/math] | Half of [math]\displaystyle{ a }[/math]: [math]\displaystyle{ a/2 }[/math] (read as "half") | One half | \widecheck{}
|
U+02C7
| |
[math]\displaystyle{ \text{-} }[/math] | [math]\displaystyle{ a\text{-} }[/math] | [math]\displaystyle{ a }[/math] negated: [math]\displaystyle{ a\text{-} }[/math] (read as "neg") | Minus sign | \text{-}
|
U+002D
| |
_ | [math]\displaystyle{ z = a + \underline{b} }[/math] | Complex part of [math]\displaystyle{ z }[/math]: [math]\displaystyle{ \underline{1}b }[/math] with imaginary unit [math]\displaystyle{ \underline{1} }[/math] (read as "comp") | Imaginary unit | \underline{}
|
U+005F
| |
[math]\displaystyle{ \nu }[/math] | [math]\displaystyle{ {}^{\nu} A }[/math] | greatest finite number: intersection of the complex or real set [math]\displaystyle{ A }[/math] for [math]\displaystyle{ {}^{\nu}\mathbb{C} := [-\nu, \; \nu] + \underline{1}[-\nu, \nu] }[/math] | Finite number | \nu
|
ν
|
U+03BD
|
[math]\displaystyle{ \omega }[/math] | [math]\displaystyle{ {}^{\omega} A }[/math] | greatest mid-finite number: intersection of the complex or real set [math]\displaystyle{ A }[/math] for [math]\displaystyle{ {}^{\omega}\mathbb{C} := [-\omega, \omega] + \underline{1}[-\omega, \omega] }[/math] | Infinite number | \omega
|
ω
|
U+03C9
|
[math]\displaystyle{ \iota }[/math] | [math]\displaystyle{ \iota = \min \mathbb{R}_{\gt 0} }[/math] | smallest positive real number | Positive number | \iota
|
ι
|
U+03B9
|
[math]\displaystyle{ {}^n }[/math] | [math]\displaystyle{ {}^n a = a^{(n)} }[/math] | [math]\displaystyle{ n }[/math]-th derivative of [math]\displaystyle{ a }[/math] (read as "n of a") | Derivative | {}^n
|
||
[math]\displaystyle{ {}_b }[/math] | [math]\displaystyle{ {}_b a = \log_b a }[/math] | Logarithm to base [math]\displaystyle{ b }[/math] for [math]\displaystyle{ a \in \mathbb{C} \setminus \mathbb{R}_{\le 0} }[/math] (read as "b log a") | Logarithm | {}_b
|
||
[math]\displaystyle{ {}_1 }[/math] | [math]\displaystyle{ {}_1 x = x/||x|| }[/math] | Unit vector to [math]\displaystyle{ x \ne 0 }[/math] | Unit vector | {}_1
|
||
[math]\displaystyle{ \infty }[/math] | [math]\displaystyle{ \infty \gg \tilde{\iota}^2 }[/math] | Replacing [math]\displaystyle{ \pm0 }[/math] by [math]\displaystyle{ \pm\widetilde{\infty} }[/math] | Infinity | \infty
|
∞
|
U+221E
|
[math]\displaystyle{ {}^{\pm} }[/math] | [math]\displaystyle{ {}^{\pm}A = A \cup \{\pm\infty\} }[/math] | Extended complex (real) set [math]\displaystyle{ A \subseteq \mathbb{K} }[/math] | Extended real number line | \pm
|
±
|
U+00B1
|
[math]\displaystyle{ \mathbb M }[/math] | [math]\displaystyle{ {\mathbb{M}}_{\mathbb{R}} = {}^{\omega}{\mathbb{R}} \setminus {}^{\nu}{\mathbb{R}} }[/math] | mid-finite numbers: [math]\displaystyle{ {\mathbb{M}}_{\mathbb{C}} := {\mathbb{M}}_{\mathbb{R}} + \underline{\mathbb{M}}_{\mathbb{R}} }[/math] | Infinite set | \mathbb{M}
|
𝕄
|
U+1D544
|
[math]\displaystyle{ {}^{\dot{}} }[/math] | [math]\displaystyle{ \dot{A} }[/math] | point-symmetric set [math]\displaystyle{ A }[/math] | Point symmetry | \dot
|
˙
|
U+02D9
|
[math]\displaystyle{ {}^{\ll} }[/math] | [math]\displaystyle{ A^{\ll} }[/math] | Set [math]\displaystyle{ A }[/math] without boundary [math]\displaystyle{ \partial A }[/math] given by min [math]\displaystyle{ \{d(x, y) : x \in A°, y \in A^{\prime}\} = \tilde{\nu} }[/math] | Boundary | {}^{\ll}
|
≪
|
U+226A
|
[math]\displaystyle{ ' }[/math] | [math]\displaystyle{ A' }[/math] | Complement of the set [math]\displaystyle{ A }[/math] | Complement | \prime
|
U+0027
| |
[math]\displaystyle{ \complement }[/math] | [math]\displaystyle{ \complement_1^n\ a_m }[/math] | Concatenation of [math]\displaystyle{ a_m }[/math] to [math]\displaystyle{ a_1, ..., a_n }[/math] | Concatenation operator | \complement
|
∁
|
U+2201
|
[math]\displaystyle{ \leftharpoonup }[/math] | [math]\displaystyle{ \overset{\leftharpoonup}{a} }[/math] | Predecessor of [math]\displaystyle{ a }[/math] (read as "pre") | Predecessor | \leftharpoonup
|
U+21BC
| |
[math]\displaystyle{ \rightharpoonup }[/math] | [math]\displaystyle{ \overset{\rightharpoonup}{a} }[/math] | Successor of [math]\displaystyle{ a }[/math] (read as "post") | Successor | \rightharpoonup
|
U+21C0
| |
[math]\displaystyle{ \upharpoonleft }[/math] | [math]\displaystyle{ a{\upharpoonleft}_n }[/math] | [math]\displaystyle{ n }[/math]-fold repetition of [math]\displaystyle{ a }[/math] in the form [math]\displaystyle{ (a, ... , a)^T }[/math] (read as "rep") | Repetition | \upharpoonleft
|
U+21BF
| |
[math]\displaystyle{ \upharpoonright }[/math] | [math]\displaystyle{ a{\upharpoonright}_n }[/math] | Projection of [math]\displaystyle{ (a_1, ... , a_n)^T }[/math] onto the [math]\displaystyle{ k }[/math]-th entry [math]\displaystyle{ a_k }[/math] (read as "proj") | Projection | \upharpoonright
|
U+21BE
| |
[math]\displaystyle{ \downarrow }[/math] | [math]\displaystyle{ \downarrow {x} }[/math] | Differential of [math]\displaystyle{ x }[/math] (read as "down") | Differential | \downarrow
|
↓
|
U+8595
|
[math]\displaystyle{ \uparrow }[/math] | [math]\displaystyle{ \uparrow f(x) }[/math] | Integral of [math]\displaystyle{ f(x) }[/math] (read as "up") | Integral | \uparrow
|
↑
|
U+8593
|
[math]\displaystyle{ \Box }[/math] | End of proof | Proof | \Box
|
U+25A1
| ||
[math]\displaystyle{ \triangle }[/math] | End of definition | Definition | \triangle
|
Δ
|
U+2206
|