- **Real Analysis**
(*http://mymathforum.com/real-analysis/*)

- - **Intermediate values theorem**
(*http://mymathforum.com/real-analysis/637-intermediate-values-theorem.html*)

Intermediate values theoremHere's a spectacular, though very easy, application of the intermediate values theorem: prove that there exist two diametrically opposed points of the earth with equal temperature (assuming the temperature is continuously distributed, and assimilating the earth to a perfect 3 dimensional ball). |

Let D(p) be the diametrically opposed point of p and let T(p) be the temperature of p.Manifestly f(p)=T(p)-T(D(p)) is a continuous function defined on a compact set, and f(D(p))=-f(p) , so there is Po such that f(Po)=0 and finally T(Po)=T(D(Po)) (q.e.d) |

All times are GMT -8. The time now is 06:40 AM. |

Copyright © 2019 My Math Forum. All rights reserved.