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<Text-field style="Heading 1" layout="Normal">ordem parcial</Text-field>
<Text-field style="Text" layout="Normal">ou <Font bold="true" encoding="UTF-8">ordena\303\247\303\243o parcial</Font>, <Font italic="true">n.</Font>  uma <Hyperlink linktarget="Dictionary:Definition/relation" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">rela\303\247\303\243o</Font></Hyperlink><Font encoding="UTF-8"> que \303\251 </Font><Hyperlink linktarget="Dictionary:Definition/reflexive" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">reflexiva</Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/antisymmetric" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">anti-sim\303\251trica</Font></Hyperlink> e <Hyperlink linktarget="Dictionary:Definition/transitive" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">transitiva</Font></Hyperlink>, <Font encoding="UTF-8">mas n\303\243o necessariamente</Font> <Hyperlink linktarget="Dictionary:Definition/connected" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">conectado</Font></Hyperlink>; <Font encoding="UTF-8">o que imp\303\265e um conjunto em uma</Font> <Hyperlink linktarget="Dictionary:Definition/lattice" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">lattice</Font></Hyperlink> (grade).  Uma ordem parcial gera <Hyperlink linktarget="Dictionary:Definition/chain" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">cadeias</Font></Hyperlink> de elementos, mas a menos que seja uma <Hyperlink linktarget="Dictionary:Definition/totalordering" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">ordena\303\247\303\243o total</Font></Hyperlink> <Font encoding="UTF-8">haver\303\241 pares de elementos do conjunto entre os quais a rela\303\247\303\243o n\303\243o seja principal em qualquer ordem, por exemplo, no diagrama de</Font> <Hyperlink linktarget="Dictionary:Definition/tree" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">\303\241rvore</Font></Hyperlink> abaixo,  onde para qualquer <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> e <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation>, <Font italic="true">x</Font> <Font family="MaplePi" encoding="UTF-8">\302\243</Font> <Font italic="true">y</Font>  se e somente se existir um caminho a partir da origem para <Font italic="true">y</Font> por <Font italic="true">x</Font>, <Font encoding="UTF-8">claramente n\303\243o \303\251 nem o caso de</Font> A <Font family="MaplePi" encoding="UTF-8">\302\243</Font> B, nem B <Font family="MaplePi" encoding="UTF-8">\302\243</Font> A.  <Font encoding="UTF-8">Em particular, embora cada cadeia finita ter\303\241 um elemento</Font> <Hyperlink linktarget="Dictionary:Definition/maximal" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">m\303\241ximo</Font></Hyperlink>  e um <Hyperlink linktarget="Dictionary:Definition/minimal" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">m\303\255nimo</Font></Hyperlink>, <Font encoding="UTF-8">estes n\303\243o podem ser exclusivos</Font>. <Font encoding="UTF-8">Por exemplo, os subconjuntos dos inteiros tem uma ordena\303\247\303\243o parcial no conjunto de</Font> <Hyperlink linktarget="Dictionary:Definition/inclusion" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">inclus\303\243o</Font></Hyperlink>; <Font encoding="UTF-8">neste caso, existe um \303\272nico elemento m\303\255nimo, o conjunto vazio, que est\303\241 contido em todos os membros do dom\303\255nio, e um elemento \303\272nico m\303\241ximo, o conjunto de n\303\272meros inteiros em si, que cont\303\251m todos os elementos do dom\303\255nio, mas n\303\243o todos os pares de elementos s\303\243o relacionados, que nem de</Font> {1, 2, 3} e <Font encoding="UTF-8">cont\303\251m o outro</Font> {2, 3, 4}. <Font encoding="UTF-8">Se o dom\303\255nio \303\251 restrito e n\303\243o-vazio a os subconjuntos pr\303\263prios, e a ordem de inclus\303\243o \303\251 rigorosa e tem um n\303\272mero infinito de elementos m\303\241ximo e m\303\255nimo. Veja tamb\303\251m</Font> <Hyperlink linktarget="Dictionary:Definition/poset" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">poset</Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/ordering" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">ordena\303\247\303\243o</Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/Zornslemma" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">Lema de Zorn</Font></Hyperlink>.  </Text-field>
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