Béda révisi "Tabel lambang matematis"

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Ngarapihkeun éjahan, replaced: rea → réa (7), ea → éa (42) using AWB
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m (Ngarapihkeun éjahan, replaced: rea → réa (7), ea → éa (42) using AWB)
 
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<table border=1 cellspacing=0>
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&rArr;<br>&rarr;</h1>
<td>[[material implication]]
<td>implies; if .. then
<td>[[propositional calculus|propositional logic]]
<tr> <td colspan=3>''A'' &rArr; ''B'' meansméans: if ''A'' is true then ''B'' is also true; if ''A'' is false then nothing is said about ''B''.<br>&rarr; may meanméan the same as &rArr;, or it may have the meaningméaning for [[Fungsi (matematik)|function]]s mentioned further down
<tr> <td colspan=3>''x'' = 2&nbsp;&nbsp;&rArr;&nbsp; ''x''<sup>2</sup> = 4 is true, but ''x''<sup>2</sup> = 4 &nbsp;&nbsp;&rArr;&nbsp; ''x'' = 2 is in general false (since ''x'' could be &minus;2)
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&hArr;<br>&harr;</h1>
<td>[[material equivalence]]
<td>if and only if; iff
<td>[[propositional calculus|propositional logic]]
<tr> <td colspan=3>''A''&nbsp;&hArr; ''B'' meansméans: ''A'' is true if ''B'' is true and ''A'' is false if ''B'' is false
<tr> <td colspan=3>''x''&nbsp;+ 5&nbsp;= ''y''&nbsp;+ 2&nbsp;&nbsp;&hArr;&nbsp; ''x''&nbsp;+ 3&nbsp;= ''y''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&and;</h1>
<td>[[logical conjunction]] or '''meet''' in a [[lattice (order)|lattice]]
<td>and
<td>[[propositional calculus|propositional logic]], [[lattice (order)|lattice theory]]
<tr> <td colspan=3>the statement ''A'' &and; ''B'' is true if ''A'' and ''B'' are both true; else it is false
<tr> <td colspan=3>''n''&nbsp;< 4&nbsp;&nbsp;&and;&nbsp; ''n''&nbsp;> 2&nbsp;&nbsp;&hArr;&nbsp; ''n''&nbsp;= 3 when <var>n</var> is a [[natural number]]
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&or;</h1>
<td>[[logical disjunction]] or '''join''' in a [[lattice (order)|lattice]]
<td>or
<td>[[propositional calculus|propositional logic]], [[lattice (order)|lattice theory]]
<tr> <td colspan=3>the statement ''A'' &or; ''B'' is true if ''A'' or ''B'' (or both) are true; if both are false, the statement is false
<tr> <td colspan=3>''n''&nbsp;&ge; 4&nbsp;&nbsp;&or;&nbsp; ''n''&nbsp;&le; 2&nbsp;&nbsp;&hArr; ''n''&nbsp;&ne; 3 when <var>n</var> is a [[natural number]]
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&not;¬<br>/</h1>
<td>[[logical negation]]
<td>not
<td>[[propositional calculus|propositional logic]]
<tr> <td colspan=3>the statement &not;¬''A'' is true if and only if ''A'' is false<br>a slash placed through another operator is the same as "&not;" placed in front
<tr> <td colspan=3>&not;¬(''A''&nbsp;&and; ''B'')&nbsp;&hArr; (&not;¬''A'')&nbsp;&or; (&not;¬''B''); <var>x</var>&nbsp;&notin; <var>S</var>&nbsp;&nbsp;&hArr;&nbsp; &not;¬(<var>x</var>&nbsp;&isin; <var>S</var>)
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&forall;</h1>
<td>[[universal quantification]]
<td>for all; for any; for eachéach
<td>[[predicate logic]]
<tr> <td colspan=3>&forall;&nbsp;''x'': ''P''(''x'') meansméans: ''P''(''x'') is true for all ''x''</tr>
<tr> <td colspan=3>&forall;&nbsp;''n''&nbsp;&isin; '''N''': ''n''<sup>2</sup>&nbsp;&ge; ''n''</tr>
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&exist;</h1>
<td>[[existential quantification]]
<td>there exists
<td>[[predicate logic]]
<tr> <td colspan=3>&exist;&nbsp;''x'': ''P''(''x'') meansméans: there is at leastléast one ''x'' such that ''P''(''x'') is true
<tr> <td colspan=3>&exist;&nbsp;''n''&nbsp;&isin; '''N''': ''n''&nbsp;+ 5&nbsp;= 2''n''
 
<tr>
<td>equals
<td>everywhere
<tr> <td colspan=3><var>x</var>&nbsp;= <var>y</var> meansméans: <var>x</var> and <var>y</var> are different names for precisely the same thing
<tr> <td colspan=3>1&nbsp;+ 2&nbsp;= 6&nbsp;&minus; 3
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>:=<br>&equiv;<br>:&hArr;</h1>
<td>[[definition]]
<td>is defined as
<td>everywhere
<tr> <td colspan=3><var>x</var>&nbsp;:= <var>y</var> or <var>x</var>&nbsp;&equiv; <var>y</var> meansméans: <var>x</var> is defined to be another name for <var>y</var> (but note that &equiv; can also meanméan other things, such as [[congruence]])<br><var>P</var>&nbsp;:&hArr; <var>Q</var> meansméans: <var>P</var> is defined to be logically equivalent to <var>Q</var>
<tr> <td colspan=3>cosh&nbsp;''x''&nbsp;:= (1/2)(exp&nbsp;''x''&nbsp;+ exp&nbsp;(&minus;''x'')); ''A'' XOR ''B''&nbsp;:&hArr; (''A''&nbsp;&or; ''B'')&nbsp;&and; &not;¬(''A''&nbsp;&and; ''B'')
 
<tr>
<td>the set of ...
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>{<var>a</var>,<var>b</var>,<var>c</var>} meansméans: the set consisting of <var>a</var>, <var>b</var>, and <var>c</var>
<tr> <td colspan=3>'''N'''&nbsp;= {0,1,2,...}
 
<td>the set of ... such that ...
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>{''x''&nbsp;: ''P''(''x'')} meansméans: the set of all ''x'' for which ''P''(''x'') is true. {''x''&nbsp;| ''P''(''x'')} is the same as {''x''&nbsp;: ''P''(''x'')}.
<tr> <td colspan=3>{''n''&nbsp;&isin; '''N'''&nbsp;: ''n''<sup>2</sup>&nbsp;<&nbsp;20}&nbsp;= {0,1,2,3,4}
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&empty;<br>{}</h1>
<td>[[empty set]]
<td>empty set
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>{} meansméans: the set with no elements; &empty; is the same thing
<tr> <td colspan=3>{''n''&nbsp;&isin; '''N'''&nbsp;: 1&nbsp;< ''n''<sup>2</sup>&nbsp;< 4}&nbsp;= {}
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&isin;<br>&notin;</h1>
<td>set membership
<td>in; is in; is an element of; is a member of; belongs to
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>''a''&nbsp;&isin; ''S'' meansméans: ''a'' is an element of the set ''S''; ''a''&nbsp;&notin; ''S'' meansméans: ''a'' is not an element of ''S''
<tr> <td colspan=3>(1/2)<sup>&minus;1</sup>&nbsp;&isin; '''N'''; 2<sup>&minus;1</sup>&nbsp;&notin; '''N'''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&sube;<br>&sub;</h1>
<td>[[subset]]
<td>is a subset of
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>''A''&nbsp;&sube; ''B'' meansméans: every element of ''A'' is also element of ''B''<br>''A''&nbsp;&sub; ''B'' meansméans: <var>A</var>&nbsp;&sube; <var>B</var> but ''A''&nbsp;&ne; ''B''
<tr> <td colspan=3>''A''&nbsp;&cap; ''B'' &sube; ''A''; '''Q'''&nbsp;&sub; '''R'''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&cup;</h1>
<td>[[set theoretic union]]
<td>the union of ... and ...; union
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>''A''&nbsp;&cup; ''B'' meansméans: the set that contains all the elements from ''A'' and also all those from ''B'', but no others
<tr> <td colspan=3>''A''&nbsp;&sube; ''B''&nbsp;&nbsp;&hArr;&nbsp; ''A''&nbsp;&cup; ''B''&nbsp;= ''B''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&cap;</h1>
<td>[[set theoretic intersection]]
<td>intersected with; intersect
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>''A''&nbsp;&cap; ''B'' meansméans: the set that contains all those elements that ''A'' and ''B'' have in common
<tr> <td colspan=3>{''x''&nbsp;&isin; '''R'''&nbsp;: ''x''<sup>2</sup>&nbsp;= 1}&nbsp;&cap; '''N'''&nbsp;= {1}
 
<tr>
<td>minus; without
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>''A''&nbsp;\ ''B'' meansméans: the set that contains all those elements of ''A'' that are not in ''B''
<tr> <td colspan=3>{1,2,3,4} \ {3,4,5,6} = {1,2}
 
<td>of
<td>[[naive set theory|set theory]]
<tr> <td colspan=3>for function application: <var>f</var>(<var>x</var>) meansméans: the value of the function <var>f</var> at the element <var>x</var><br>for grouping: perform the operations inside the parentheses first
<tr> <td colspan=3>If <var>f</var>(<var>x</var>)&nbsp;:= <var>x</var><sup>2</sup>, then <var>f</var>(3)&nbsp;= 3<sup>2</sup>&nbsp;= 9; (8/4)/2&nbsp;= 2/2&nbsp;= 1, but 8/(4/2)&nbsp;= 8/2&nbsp;= 4
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>''f'':''X''&rarr;''Y''</h1>
<td>function arrow
<td>from ... to
<td>[[function (mathematics)|function]]s
<tr> <td colspan=3><var>f</var>:&nbsp;<var>X</var>&nbsp;&rarr; <var>Y</var> meansméans: the function <var>f</var> maps the set <var>X</var> into the set <var>Y</var>
<tr> <td colspan=3>Consider the function <var>f</var>:&nbsp;<b>'''Z</b>'''&nbsp;&rarr; <b>'''N</b>''' defined by <var>f</var>(<var>x</var>)&nbsp;= <var>x</var><sup>2</sup>
 
<tr>
<td>N
<td>[[number]]s
<tr> <td colspan=3>'''N''' meansméans {0,1,2,3,...}, but see the article on [[natural number]]s for a different convention.
<tr> <td colspan=3>{|''a''|&nbsp;: ''a''&nbsp;&isin; '''Z'''}&nbsp;= '''N'''
 
<tr>
<td>Z
<td>[[number]]s
<tr> <td colspan=3>'''Z''' meansméans: {...,&minus;3,&minus;2,&minus;1,0,1,2,3,...}
<tr> <td colspan=3>{''a''&nbsp;: |''a''|&nbsp;&isin; '''N'''}&nbsp;= '''Z'''
 
<tr>
<td>Q
<td>[[number]]s
<tr> <td colspan=3>'''Q''' meansméans: {''p''/''q''&nbsp;: ''p'',''q''&nbsp;&isin; '''Z''', ''q''&nbsp;&ne; 0}
<tr> <td colspan=3>3.14&nbsp;&isin; '''Q'''; &pi;π&nbsp;&notin; '''Q'''
 
<tr>
<td>R
<td>[[number]]s
<tr> <td colspan=3>'''R''' meansméans: {lim<sub>n&rarr;&infin;n→∞</sub>&nbsp;''a''<sub>''n''</sub>&nbsp;: &forall;&nbsp;''n''&nbsp;&isin; <b>'''N</b>''': <var>a</var><sub>''n''</sub>&nbsp;&isin; <b>'''Q</b>''', the limit exists}
<tr> <td colspan=3>&pi;π&nbsp;&isin; '''R'''; &radic;(&minus;1)&nbsp;&notin; '''R'''
 
<tr>
<td>C
<td>[[number]]s
<tr> <td colspan=3>'''C''' meansméans: {''a''&nbsp;+ ''bi''&nbsp;: ''a'',''b''&nbsp;&isin; '''R'''}
<tr> <td colspan=3>''i''&nbsp;= &radic;(&minus;1)&nbsp;&isin; '''C'''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&lt;<br>&gt;</h1>
<td>comparison
<td>is less than, is greatergréater than
<td>[[partial order]]s
<tr> <td colspan=3>''x''&nbsp;&lt; ''y'' meansméans: ''x'' is less than ''y''; ''x''&nbsp;> ''y'' meansméans: ''x'' is greatergréater than ''y''
<tr> <td colspan=3>''x''&nbsp;&lt; ''y''&nbsp;&nbsp;&hArr;&nbsp; <var>y</var>&nbsp;&gt; <var>x</var>
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&le;<br>&ge;</h1>
<td>comparison
<td>is less than or equal to, is greatergréater than or equal to
<td>[[partial order]]s
<tr> <td colspan=3><var>x</var>&nbsp;&le; <var>y</var> meansméans: <var>x</var> is less than or equal to <var>y</var>; ''x''&nbsp;&ge; ''y'' meansméans: ''x'' is greatergréater than or equal to ''y''
<tr> <td colspan=3>''x''&nbsp;&ge; 1&nbsp;&nbsp;&rArr;&nbsp; ''x''<sup>2</sup>&nbsp;&ge; ''x''
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&radic;</h1>
<td>[[square root]]
<td>the principal square root of; square root
<td>[[real numbers]]
<tr> <td colspan=3>&radic;''x'' meansméans: the positive number whose square is ''x''
<tr> <td colspan=3>&radic;(''x''<sup>2</sup>)&nbsp;= |''x''|
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&infin;</h1>
<td>[[infinity]]
<td>infinity
<td>[[number]]s
<tr> <td colspan=3>&infin; is an element of the [[extended real number line|extended number line]] that is greatergréater than all realréal numbers; it often occurs in [[mathematical limit|limits]]
<tr> <td colspan=3>lim<sub>x&rarr;0x→0</sub>&nbsp;1/|''x''|&nbsp;= &infin;
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&pi;π</h1>
<td>[[pi]]
<td>pi
<td>[[Euclidean geometry]]
<tr> <td colspan=3>&pi;π meansméans: the ratio of a [[circle]]'s circumference to its diameter
<tr> <td colspan=3>''A''&nbsp;= &pi;π''r''&sup2;² is the areaaréa of a circle with radius ''r''
 
<tr>
<td>absolute value of
<td>[[number]]s
<tr> <td colspan=3>|<var>x</var>| meansméans: the distance in the [[real line]] (or the [[complex plane]]) between <var>x</var> and [[zero]]
<tr> <td colspan=3>|''a''&nbsp;+ ''bi''|&nbsp;= &radic;(''a''<sup>2</sup>&nbsp;+ ''b''<sup>2</sup>)
 
<tr>
<td>[[functional analysis]]
<tr> <td colspan=3>||<var>x</var>|| is the norm of the element ''x'' of a [[normed vector space]]
<tr> <td colspan=3>||''x''+''y''|| &le; ||''x''|| + ||''y''||
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&sum;</h1>
<td>[[addition|summation]]
<td>sum over ... from ... to ... of
<td>[[arithmetic]]
<tr> <td colspan=3>&sum;<sub>''k''=1</sub><sup>''n''</sup>&nbsp;''a''<sub>''k''</sub> meansméans: ''a''<sub>1</sub>&nbsp;+ ''a''<sub>2</sub>&nbsp;+ ...&nbsp;+ ''a''<sub>''n''</sub>
<tr> <td colspan=3>&sum;<sub>''k''=1</sub><sup>4</sup>&nbsp;''k''<sup>2</sup>&nbsp;= 1<sup>2</sup>&nbsp;+ 2<sup>2</sup>&nbsp;+ 3<sup>2</sup>&nbsp;+ 4<sup>2</sup>&nbsp;= 1&nbsp;+ 4&nbsp;+ 9&nbsp;+ 16&nbsp;= 30
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&prod;</h1>
<td>[[multiplication|product]]
<td>product over ... from ... to ... of
<td>[[arithmetic]]
<tr> <td colspan=3>&prod;<sub>''k''=1</sub><sup>''n''</sup>&nbsp;''a''<sub>''k''</sub> meansméans: ''a''<sub>1</sub>''a''<sub>2</sub>&middot;&middot;&middot;···''a''<sub>''n''</sub>
<tr> <td colspan=3>&prod;<sub>''k''=1</sub><sup>4</sup>&nbsp;(''k''&nbsp;+ 2)&nbsp;= (1&nbsp; + 2)(2&nbsp;+ 2)(3&nbsp;+ 2)(4&nbsp;+ 2)&nbsp;= 3&nbsp;&times; 4&nbsp;&times; 5&nbsp;&times; 6&nbsp;= 360
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&int;</h1>
<td>[[integration]]
<td>integral from ... to ... of ... with respect to
<td>[[calculus]]
<tr> <td colspan=3>&int;<sub>''a''</sub><sup>''b''</sup>&nbsp;''f''(''x'')&nbsp;d''x'' meansméans: the signed [[area]] between the ''x''-axis and the [[graph (functions)|graph]] of the [[Fungsi (matematik)|function]] ''f'' between <var>x</var>&nbsp;= ''a'' and <var>x</var>&nbsp;= ''b''
<tr> <td colspan=3>&int;<sub>0</sub><sup>''b''</sup>&nbsp;x<sup>2</sup>&nbsp;d''x''&nbsp;= ''b''<sup>3</sup>/3; &int;''x''<sup>2</sup>&nbsp;d''x''&nbsp;= ''x''<sup>3</sup>/3
 
<tr>
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&#8711;</h1>
<td>[[gradient]]
<td>[[del]], [[nabla]], [[gradient]] of
<td>[[calculus]]
<tr> <td colspan=3>&#8711;''f'' (x<sub>1</sub>, &hellip;, x<sub>''n''</sub>) is the vector of partial derivatives (''df'' / ''dx''<sub>1</sub>, &hellip;, ''df'' / ''dx''<sub>''n''</sub>)
<tr> <td colspan=3>If ''f'' (''x'',''y'',''z'') = 3''xy'' + ''z''&sup2;² then &#8711;''f'' = (3''y'', 3''x'', 2''z'')<br>
A transparent image for text is: Image:Del.svg ([[Image:Del.svg]]).
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&#8706;</h1>
<td>[[Partial derivative|partial]]
<td>partial derivative of
<td>[[calculus]]
<tr> <td colspan=3> With ''f'' (x<sub>1</sub>, &hellip;, x<sub>''n''</sub>), &#8706;f∂f/&#8706;x∂x<sub>i</sub> is the derivative of ''f'' with respect to x<sub>i</sub>, with all other variables kept constant.
<tr> <td colspan=3> If ''f''(x,y) = x<sup>2</sup>y, then &#8706;''f''/&#8706;x∂x = 2xy
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&perp;</h1>
<td>[[perpendicular]]
<td>is perpendicular to
<td>[[orthogonality]]
<tr> <td colspan=3>''x'' &perp; ''y'' meansméans: ''x'' is perpendicular to ''y''; or more generally ''x'' is orthogonal to ''y''.
<tr> <td colspan=3>
 
<tr>
<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&perp;</h1>
<td>[[bottom element]]
<td>the bottom element
<td>[[Lattice (order)|lattice theory]]
<tr> <td colspan=3>''x'' = &perp; meansméans: ''x'' is the smallest element.
<tr> <td colspan=3>
 
 
==Tumbu kaluar==
* Jeff Miller: ''Earliestéarliest Uses of Various Mathematical Symbols, http://web.archive.org/20081204035420/members.aol.com/jeff570/mathsym.html
* TCAEP - Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm