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 | Science Articles, Homework Help, Discussion**

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

**Physics Forums | Science Articles, Homework Help, Discussion**