I am struggling to understand the proof for integer parts of real numbers. I have used to mean less than or equal to because I could not work out how to type it in. I need to show that:(adsbygoogle = window.adsbygoogle || []).push({});

∃ unique n ∈ Z s.t. nx<n+1

The proof given is the following:

Let

A={k∈Z : kx}

This is a non-empty subset of R that is bounded above. Let α = sup A. There is an n ∈ A such that n > a - 1/2. n>α−1. Then nx and,since n+1>α+1>α, n+1̸∈A. Hence,n+1>x.

In particular I don't understand how A is bounded above, because I thought A = [k,∞) which has no upper bound. Where have I gone wrong?

**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!

# Proof of Integer Parts of Real numbers

Loading...

Similar Threads for Proof Integer Parts | Date |
---|---|

B Proof of a limit rule | Dec 19, 2017 |

B Proof of quotient rule using Leibniz differentials | Jun 10, 2017 |

B Don't follow one small step in proof | Jun 10, 2017 |

Addition property of integration intervals proof | Feb 26, 2015 |

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