Thomae's function
function that is discontinuous at rationals and continuous at irrationals
| rdfs:label |
"Thomae's function"@en
|
|
skos:alt |
"Thomae function"@en
|
| schema:description |
"function that is discontinuous at rationals and continuous at irrationals"@en
|
|
schema:date |
"2026-09-06T10:06:33+00:00"^^xsd:dateTime |
| schema:version | 2541004710 |
| wikibase:identifiers | 2 |
| wikibase:sitelinks | 20 |
| wikibase:statements | 12 |
| p:P138 | wd:statement/q776401-47BA1500-48C9-4D9E-A6AC-6E7BAABFF3A6 |
| p:P1568 | wd:statement/Q776401-d66eea32-4965-d1be-4d96-c032ec8801ef |
| p:P1571 | wd:statement/Q776401-fd76c1dd-49fc-cd2b-b17d-8c645854068e |
| p:P1889 | wd:statement/Q776401-B3741A80-178C-4668-A16C-FB4723921E7E |
| p:P2534 | wd:statement/Q776401-8dcbc213-41c1-ce06-03c0-a96fc65e8cdd |
| p:P31 | wd:statement/Q776401-268d0642-4fd1-e5c2-a6bb-3fa19dd72873 |
| wd:statement/Q776401-72994765-46ae-d37a-57d6-7c22bac6873a | |
| wd:statement/Q776401-90c42a24-4cc3-c65c-3528-a11d60b517e6 | |
| p:P373 | wd:statement/Q776401-50fd3d66-4d1e-21a4-dc18-cab34a2cdc23 |
| p:P6104 | wd:statement/Q776401-58F30912-80DA-4F0B-97DB-F8EDDFCEE9C0 |
| p:P6366 | wd:statement/Q776401-4C4CABC2-B0DA-4AA3-A645-EEFCABAB5824 |
| p:P646 | wd:statement/Q776401-D89E11B3-D84D-4585-955F-156CD6ABA1DA |
|
p:direct- |
<https:/ |
| wdt:P138 | Carl Johannes Thomae |
| wdt:P1568 | set of real numbers |
| wdt:P1571 | unit interval |
| wdt:P1889 | Riemann zeta function |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN">{</mo><mtable columnspacing="1em" rowspacing="4pt" columnalign="left left"><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>if </mtext></mrow><mi>x</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mstyle displaystyle="false" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></mfrac></mrow></mstyle></mrow><mspace width="1em"></mspace><mo stretchy="false">(</mo><mi>x</mi><mrow data-mjx-texclass="ORD"><mtext> is rational), with </mtext></mrow><mi>p</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℤ</mi></mrow><mrow data-mjx-texclass="ORD"><mtext> and </mtext></mrow><mi>q</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℕ</mi></mrow><mrow data-mjx-texclass="ORD"><mtext> coprime</mtext></mrow></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>if </mtext></mrow><mi>x</mi><mrow data-mjx-texclass="ORD"><mtext> is irrational.</mtext></mrow></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | function |
| periodic function | |
| mathematical concept | |
| wdt:P373 | "Thomae's function" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "34117566" |
| wdt:P646 | "/m/099fsd" |
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