Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am reading "mathematical analysis" by Apostol right now for a course in analysis. Since I am trying to understand the author's proof of the above theorem(3.25 in the book), but I have something that I can't understand.

He assumes that each of the nested sets contains infinitely many points, "...otherwise, the proof is trivial". I can't see why it's trivial and how to prove it. I would be grateful to understand why an infinite intersection of finite sets is non-empty.

Thank you.

**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!

# I Cantor's intersection theorem (Apostol)

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Cantor's intersection theorem | Date |
---|---|

Transversal Intersection of More than 2 Surfaces | Jul 4, 2015 |

Hausdorff dimension of the cantor set | Sep 14, 2013 |

Cantor Set - Perfect and Totally Disconnected | Jan 10, 2013 |

Cantor set | Aug 19, 2012 |

Why does cantors theorem not prove the interval (0,1) in Q uncountable? | Apr 18, 2012 |

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