Tabel lambang matematis: Béda antarrépisi

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<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&rArr;⇒<br>&rarr;→</h1>

<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''² = 4 is true, but ''x''² = 4 &nbsp;&nbsp;&rArr;⇒&nbsp; ''x'' = 2 is in general false (since ''x'' could be &minus;2)

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&hArr;⇔<br>&harr;↔</h1>

<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''

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&and;∧</h1>

<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]]

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&or;∨</h1>

<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]]

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&not;¬<br>/</h1>

<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>)

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&forall;∀</h1>

<td>for all; for any; for eachéach

<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''²&nbsp;&ge;≥ ''n''</tr>

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&exist;∃</h1>

<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 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

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>:=<br>&equiv;≡<br>:&hArr;⇔</h1>

<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 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>{''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''²&nbsp;<&nbsp;20}&nbsp;= {0,1,2,3,4}

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&empty;∅<br>{}</h1>

<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''²&nbsp;< 4}&nbsp;= {}

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&isin;∈<br>&notin;∉</h1>

<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)^&minus;1&nbsp;&isin;∈ '''N'''; 2^&minus;1&nbsp;&notin;∉ '''N'''

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&sube;⊆<br>&sub;⊂</h1>

<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'''

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&cup;∪</h1>

<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''

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&cap;∩</h1>

<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''²&nbsp;= 1}&nbsp;&cap;∩ '''N'''&nbsp;= {1}

<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>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

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>''f'':''X''&rarr;→''Y''</h1>

<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>²

<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 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 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 colspan=3>'''R''' meansméans: {lim_{n&rarr;&infin;n→∞}&nbsp;''a''_''n''&nbsp;: &forall;∀&nbsp;''n''&nbsp;&isin;∈ <b>'''N</b>''': <var>a</var>_''n''&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 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'''

<td>is less than, is greatergréater than

<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>

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&le;≤<br>&ge;≥</h1>

<td>is less than or equal to, is greatergréater than or equal to

<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''²&nbsp;&ge;≥ ''x''

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&radic;√</h1>

<tr> <td colspan=3>&radic;√''x'' meansméans: the positive number whose square is ''x''

<tr> <td colspan=3>&radic;√(''x''²)&nbsp;= |''x''|

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&infin;∞</h1>

<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_{x&rarr;0x→0}&nbsp;1/|''x''|&nbsp;= &infin;∞

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&pi;π</h1>

<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 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''²&nbsp;+ ''b''²)

<tr> <td colspan=3>||''x''+''y''|| &le;≤ ||''x''|| + ||''y''||

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&sum;∑</h1>

<tr> <td colspan=3>&sum;∑_''k''=1^''n''&nbsp;''a''_''k'' meansméans: ''a''₁&nbsp;+ ''a''₂&nbsp;+ ...&nbsp;+ ''a''_''n''

<tr> <td colspan=3>&sum;∑_''k''=1⁴&nbsp;''k''²&nbsp;= 1²&nbsp;+ 2²&nbsp;+ 3²&nbsp;+ 4²&nbsp;= 1&nbsp;+ 4&nbsp;+ 9&nbsp;+ 16&nbsp;= 30

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&prod;∏</h1>

<tr> <td colspan=3>&prod;∏_''k''=1^''n''&nbsp;''a''_''k'' meansméans: ''a''₁''a''₂&middot;&middot;&middot;···''a''_''n''

<tr> <td colspan=3>&prod;∏_''k''=1⁴&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

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&int;∫</h1>

<tr> <td colspan=3>&int;∫_''a''^''b''&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;∫₀^''b''&nbsp;x²&nbsp;d''x''&nbsp;= ''b''³/3; &int;∫''x''²&nbsp;d''x''&nbsp;= ''x''³/3

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&#8711;∇</h1>

<tr> <td colspan=3>&#8711;∇''f'' (x₁, &hellip;…, x_''n'') is the vector of partial derivatives (''df'' / ''dx''₁, &hellip;…, ''df'' / ''dx''_''n'')

<tr> <td colspan=3>If ''f'' (''x'',''y'',''z'') = 3''xy'' + ''z''&sup2;² then &#8711;∇''f'' = (3''y'', 3''x'', 2''z'')<br>

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&#8706;∂</h1>

<tr> <td colspan=3> With ''f'' (x₁, &hellip;…, x_''n''), &#8706;f∂f/&#8706;x∂x_i is the derivative of ''f'' with respect to x_i, with all other variables kept constant.

<tr> <td colspan=3> If ''f''(x,y) = x²y, then &#8706;∂''f''/&#8706;x∂x = 2xy

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&perp;⊥</h1>

<tr> <td colspan=3>''x'' &perp;⊥ ''y'' meansméans: ''x'' is perpendicular to ''y''; or more generally ''x'' is orthogonal to ''y''.

<td rowspan=3 bgcolor=#d0f0d0 align=center><h1>&perp;⊥</h1>

<tr> <td colspan=3>''x'' = &perp;⊥ meansméans: ''x'' is the smallest element.

* Jeff Miller: ''Earliestéarliest Uses of Various Mathematical Symbols, http://web.archive.org/20081204035420/members.aol.com/jeff570/mathsym.html