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Cantor set
Image: Wikimedia Commons

Cantor set

Fractal and set of points on a line segment

Entitynull setdiscontinuumQ273188

Also known as Cantor sets · Cantor ternary set

Instance of
Subclass of
Part of

All data

24 statements · 0% with external sources · numbers in brackets are citations

In defining formula
  • <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"><mo>lim</mo></mstyle></mrow></math>
  • <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"><mo stretchy="false">∪</mo></mstyle></mrow></math>
  • <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"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒞</mi></mrow></mstyle></mrow></math>
  • <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"><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mstyle></mrow></math>
Defining formula
  • <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"><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">:=</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">]</mo><mo>,</mo><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">:=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mo stretchy="false">∪</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒞</mi></mrow><mo stretchy="false">:=</mo><munder><mo form="prefix">lim</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false" accent="false">→</mo><mi mathvariant="normal">∞</mi></mrow></mrow></munder><msub><mi>C</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mstyle></mrow></math>
Set cardinality
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Named after

On other databases

13 identifiers linking Cantor set across the web's reference databases