Pengguna:Klasüo/bak pasir/templat: Perbedaan antara revisi
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{| class="wikitable collapsible <includeonly>{{#ifeq:{{{1|}}}|expanded | |collapsed}}</includeonly>" <!-- |
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-->style="table-layout:auto; width:1%; {{#switch:{{{position|}}} |center|centre=margin-left:auto; margin-right:auto; |#default=float:{{{position|right}}};}} margin-top:0; padding-top:0;" |
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|- |
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! style="padding-left:0.5em; padding-right:0.5em;" | [[Relasi transitif|Transitif]] [[relasi biner]] |
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|- |
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| {{Aligned table |
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| cols = 10 |
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| style = text-align:center; |
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| rowstyle = vertical-align:middle; |
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| col1align = right |
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| col1style = padding-left:0.6em; padding-right:1.2em; font-weight:bold; |
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| row1style = padding-left:0.3em; padding-right:0.3em;<!-- font-weight:bold;--> |
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| |
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| [[Relasi simetri|Simetris]] |
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| [[Relasi antisimetri|Antisimetris]] |
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| [[Relasi terhubung|Terhubung]] |
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| [[Relasi paut rapi|Paut rapu]] |
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| [[Sambungan dan pertemuan (matematika)|Sambungan]] |
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| [[Sambungan dan pertemuan (matematika)|Pertemuan]] |
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| [[Relasi refleksif|Refleksif]] |
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| [[Relasi refleksif#Irrefleksif|Irefleksif]] |
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| [[Relasi asimetri|Asimetris]] |
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| | | | Total, Semiterhubung | | | | | Anti-<br/>refleksif | |
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<!------------------------------------------------------------------------------------------------- |
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sim antisim total pautrapi sambungan pertemuan refleks irrefleks asim |
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--------------------------------------------------------------------------------------------------> |
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| {{nowrap|[[Relasi ekuivalen]]}} |
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| {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| {{nowrap|[[Praurutan|Praurutan {{smaller|(Urutan semu)}}]]}} |
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| {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Urutan parsial]] |
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| {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Praurutan total]] |
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| {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Urutan total]] |
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| {{n&}} | {{aye}} | {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Praurutanrapi]] |
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| {{n&}} | {{n&}} | {{aye}} | {{aye}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| {{nowrap|[[Urutan kuasi rapi]]}} |
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| {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Urutan rapi]] |
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| {{n&}} | {{aye}} | {{aye}} | {{aye}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Kekisi (urutan)|Kekisi]] |
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| {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{aye}} | {{aye}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Semikekisi sambungan]] |
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| {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} |
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| [[Semikekisi pertemuan]] |
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| {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{aye}} | {{n&}} | {{n&}} |
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<!-- |
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| | | | | | | | | | |
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| | | | | | | | | | |
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--> |
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| [[Strict partial order]] |
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| {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{aye}} |
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| [[Weak ordering#Strict weak orderings|Strict weak order]] |
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| {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{aye}} |
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| [[Strict total order]] |
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| {{n&}} | {{n&}} | {{aye}} | {{n&}} | {{n&}} | {{n&}} | {{n&}} | {{aye}} | {{aye}} |
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<!------------------------------------------------------------------------------------------------- |
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sym antisym total wellfound joins meets reflex irreflex asym |
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--------------------------------------------------------------------------------------------------> |
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| |
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| [[Symmetric relation|Symmetric]] |
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| [[Antisymmetric relation|Antisymmetric]] |
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| [[Connected relation|Connected]] |
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| [[Well-founded relation|Well-founded]] |
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| [[Join and meet|Has joins]] |
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| [[Join and meet|Has meets]] |
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| [[Reflexive relation|Reflexive]] |
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| [[Reflexive relation#Irreflexive|Irreflexive]] |
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| [[Asymmetric relation|Asymmetric]] |
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| Definitions, <br/>for all <math>a, b</math> and <math>S\neq\varnothing</math>: |
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| <math>\begin{align}&aRb \\ \Rightarrow{} &bRa\end{align}</math> |
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| <math>\begin{align}aRb\text{ and }&bRa \\ \Rightarrow a ={} &b\end{align}</math> |
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| <math>\begin{align}a \neq{} &b \Rightarrow \\ aRb\text{ or }&bRa\end{align}</math> |
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| <math>\begin{align}\min S \\ \text{exists}\end{align}</math> |
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| <math>\begin{align}a \vee b \\ \text{exists}\end{align}</math> |
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| <math>\begin{align}a \wedge b \\ \text{exists}\end{align}</math> |
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| <math>aRa</math> |
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| <math>\text{not }aRa</math> |
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| <math>\begin{align}aRb \Rightarrow \\ \text{not }bRa\end{align}</math> |
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}} |
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|- |
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| style="text-align:center;" | {{aye}} indicates that the column's property is required by the definition of the row's term (at the very left). For example, the definition of an equivalence relation requires it to be symmetric. All definitions tacitly require the [[homogeneous relation]] <math>R</math> be [[transitive relation|transitive]]: for all <math>a, b, c,</math> if <math>aRb</math> and <math>bRc</math> then <math>aRc,</math> and there are [[homogeneous relation|additional properties]] that a homogeneous relation may satisfy. |
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|}<noinclude> |
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{{Documentation |
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| content = |
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Template's default state when [[Wikipedia:Transclusion|transcluded]] is collapsed. To override, invoke as <code><nowiki>{{Binary relations |expanded}}</nowiki></code>. |
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To change the template's position from the default shown, add the parameter ''position'' with the value "left", "center", "centre" or "right". |
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[[Category:Mathematics sidebar templates]] |
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}}</noinclude> |
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