data/68.json
{
"definitions" : {
"P_{x}" : [ "poset", { } ],
"P" : [ {
"Q474715" : "partially ordered set (a set ordered by a transitive, antisymmetric, and reflexive binary relation)"
} ],
"a" : [ {
"Q379825" : "element (any one of the distinct objects that make up a set in set theory)"
} ],
"x" : [ "point", {
"Q379825" : "element (any one of the distinct objects that make up a set in set theory)"
} ]
},
"constraints" : [ ],
"math_inputtex" : " P_x = P - \\{ a\\mid a \\geq x\\} ",
"math_inputtex_semantic" : "\\w{Q474715}{P}_{\\wf{Q379825}{x}} = P - \\{ \\w{Q379825}{a} \\mid a \\geq x\\}",
"correct_tex" : " P_x = P - \\{ a\\mid a \\geq x\\} ",
"correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"P_{x}=P-\\{a\\mid a\\geq x\\}\" display=\"inline\">\n <semantics id=\"p1.1.m1.1a\">\n <mrow id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">\n <msub id=\"p1.1.m1.1.13.1\" xref=\"p1.1.m1.1.13.1.cmml\">\n <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">P</mi>\n <mi id=\"p1.1.m1.1.2.1\" xref=\"p1.1.m1.1.2.1.cmml\">x</mi>\n </msub>\n <mo id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">=</mo>\n <mrow id=\"p1.1.m1.1.13.2\" xref=\"p1.1.m1.1.13.2.cmml\">\n <mi id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">P</mi>\n <mo id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">-</mo>\n <mrow id=\"p1.1.m1.1.13.2.1\" xref=\"p1.1.m1.1.13.2.1.1.cmml\">\n <mo stretchy=\"false\" id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.13.2.1.1.1.cmml\">{</mo>\n <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">a</mi>\n <mo id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.13.2.1.1.1.cmml\">∣</mo>\n <mrow id=\"p1.1.m1.1.13.2.1.2\" xref=\"p1.1.m1.1.13.2.1.2.cmml\">\n <mi id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">a</mi>\n <mo id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">≥</mo>\n <mi id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.11.cmml\">x</mi>\n </mrow>\n <mo stretchy=\"false\" id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.13.2.1.1.1.cmml\">}</mo>\n </mrow>\n </mrow>\n </mrow>\n <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n <apply id=\"p1.1.m1.1.13.cmml\" xref=\"p1.1.m1.1.13\">\n <eq id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\"/>\n <apply id=\"p1.1.m1.1.13.1.cmml\" xref=\"p1.1.m1.1.13.1\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.13.1.1.cmml\" xref=\"p1.1.m1.1.13.1\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q474715</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.2.1.cmml\" xref=\"p1.1.m1.1.2.1\">Q379825</csymbol>\n </apply>\n <apply id=\"p1.1.m1.1.13.2.cmml\" xref=\"p1.1.m1.1.13.2\">\n <minus id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\"/>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">Q474715</csymbol>\n <apply id=\"p1.1.m1.1.13.2.1.1.cmml\" xref=\"p1.1.m1.1.13.2.1\">\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.13.2.1.1.1.cmml\" xref=\"p1.1.m1.1.6\">conditional-set</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q379825</csymbol>\n <apply id=\"p1.1.m1.1.13.2.1.2.cmml\" xref=\"p1.1.m1.1.13.2.1.2\">\n <geq id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\"/>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">Q379825</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\">Q379825</csymbol>\n </apply>\n </apply>\n </apply>\n </apply>\n </annotation-xml>\n <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">P_{x}=P-\\{a\\mid a\\geq x\\}</annotation>\n </semantics>\n</math>",
"uri" : "https://en.formulasearchengine.com/w/index.php?oldid=27027#math27027.0",
"title" : "Poset_game",
"comment" : "P_{x} is a substitution",
"type" : "relation"
}