Let C be the Cantor set(adsbygoogle = window.adsbygoogle || []).push({});

Let A be the set which is the union of those end points of each interval in each step of the cantor set construction

It seems to be true that A is countable and C is uncountable. Moreover, A is a proper subset of C. But I cannot imagin what kind of the points in C - A should be, for if p is not an end point of some interval, p seems to be an interior point of some interval but contor set contains no segment. Is there any way to understand these points besides using an ternary expansion to prove that C is uncountable and hence ponits like this simply exist?

Any help would be appreciated

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about Cantor Set

Loading...

Similar Threads - Question Cantor | Date |
---|---|

I Question about simplifying Sigma notation | Feb 11, 2018 |

I Shopping List Game: Probability Question | Dec 10, 2017 |

I A simple question about probability theory | Aug 2, 2017 |

One more question about the cantor set. | Jan 7, 2012 |

Questions re Cantor Set | Sep 6, 2008 |

**Physics Forums - The Fusion of Science and Community**