It is relatively simple to prove the squeeze theorem on the reals, using the usual metric. My question is, can you prove the squeeze theorem on R for an arbitrary metric (on R)? Does this even hold for an arbitrary metric on R? It seems to me that part way through the proof, you would need to show that x<=y<=z implies both that d(x,y)<=d(x,z) and d(y,z)<=d(x,z), where d is the metric. I'm not sure wether or not this is true for an arbitrary metric because I've had little experience with metrics on R other than the usual one. Is there a way to prove this/ is it even true? Thanks for any help/insights.(adsbygoogle = window.adsbygoogle || []).push({});

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

Join Physics Forums Today!

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

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

# Squeeze Theorem for an arbitrary metric

Loading...

Similar Threads for Squeeze Theorem arbitrary | Date |
---|---|

Squeeze Theorem | Sep 29, 2015 |

Squeeze Theorem: What does it mean for a function to be less than or greater than a another function | Oct 5, 2014 |

Confusion about squeeze theorem example; plugging 0 into x when x ≠ 0. | Jun 7, 2012 |

Examples of squeeze theorem | Aug 1, 2011 |

How would I explain what scenarios the squeeze theorem should be used in? | Jun 29, 2011 |

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