ag-gipp/GoUldI

{
  "definitions": {
    "W": [
      {
        "Q7913892": "Van der Waerden number"
      }
    ],
    "k": [
      {
        "Q12503": "integer (number that can be written without a fractional or decimal component)"
      }
    ],
    "\\varepsilon": [
      {
        "Q3176558": "positive number (real number strictly greater than zero)"
      }
    ]
  },
  "constraints": [],
  "math_inputtex": "W(2, k) > 2^k/k^\\varepsilon",
  "math_inputtex_semantic": "\\wf{Q7913892}{W}(2, \\w{Q12503}{k}) > {2}^{k}/{k}^{\\w{Q3176558}{\\varepsilon}}",
  "correct_tex": "W(2, k) > 2^k/k^\\varepsilon",
  "correct_mml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"W(3,k)&gt;{2}^{k}/{k}^{\\varepsilon}\" 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      <mrow id=\"p1.1.m1.1.13.1.2\" xref=\"p1.1.m1.1.13.1.1.cmml\">\n        <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">W</mi>\n        <mo id=\"p1.1.m1.1.13.1.2a\" xref=\"p1.1.m1.1.13.1.1.cmml\">⁡</mo>\n        <mrow id=\"p1.1.m1.1.13.1.2.1\" xref=\"p1.1.m1.1.13.1.1.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.13.1.1.cmml\">(</mo>\n          <mn id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">3</mn>\n          <mo id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.13.1.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">k</mi>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.13.1.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">&gt;</mo>\n      <mrow id=\"p1.1.m1.1.13.2\" xref=\"p1.1.m1.1.13.2.cmml\">\n        <msup id=\"p1.1.m1.1.13.2.1\" xref=\"p1.1.m1.1.13.2.1.cmml\">\n          <mn id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">2</mn>\n          <mi id=\"p1.1.m1.1.9.1\" xref=\"p1.1.m1.1.9.1.cmml\">k</mi>\n        </msup>\n        <mo id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">/</mo>\n        <msup id=\"p1.1.m1.1.13.2.2\" xref=\"p1.1.m1.1.13.2.2.cmml\">\n          <mi id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.11.cmml\">k</mi>\n          <mi id=\"p1.1.m1.1.12.1\" xref=\"p1.1.m1.1.12.1.cmml\">ε</mi>\n        </msup>\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        <gt id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\"/>\n        <apply id=\"p1.1.m1.1.13.1.1.cmml\" xref=\"p1.1.m1.1.13.1.2\">\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q7913892</csymbol>\n          <cn type=\"integer\" id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">3</cn>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\">Q12503</csymbol>\n        </apply>\n        <apply id=\"p1.1.m1.1.13.2.cmml\" xref=\"p1.1.m1.1.13.2\">\n          <divide id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\"/>\n          <apply id=\"p1.1.m1.1.13.2.1.cmml\" xref=\"p1.1.m1.1.13.2.1\">\n            <power xmlns:m=\"http://www.w3.org/1998/Math/MathML\" xref=\"p1.1.m1.1.13.2.1\"/>\n            <cn type=\"integer\" id=\"p1.1.m1.1.8.cmml\" xref=\"p1.1.m1.1.8\">2</cn>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.9.1.cmml\" xref=\"p1.1.m1.1.9.1\">Q12503</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.13.2.2.cmml\" xref=\"p1.1.m1.1.13.2.2\">\n            <power xmlns:m=\"http://www.w3.org/1998/Math/MathML\" xref=\"p1.1.m1.1.13.2.2\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\">Q12503</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.12.1.cmml\" xref=\"p1.1.m1.1.12.1\">Q3176558</csymbol>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">W(3,k)&gt;{2}^{k}/{k}^{\\varepsilon}</annotation>\n  </semantics>\n</math>",
  "uri": "https://en.formulasearchengine.com/w/index.php?oldid=2459#math2459.3",
  "title": "Van_der_Waerden's_theorem",
  "comment": "",
  "type": "relation",
  "check": {
    "tree": true,
    "qid": true
  }
}