(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that any rational in the interval (0,1] can be expressed as a finite sum r=1/q_{1}+1/q_{2}+...+1/q_{n}where the q_{j}are integers and q_{1}<q_{2}<...<q_{n}.

2. Relevant equations

3. The attempt at a solution

Let x[itex]\in[/itex]and 0<x[itex]\leq[/itex]1.Q

Prove [itex]\exists[/itex]q_{1}, q_{2}, ..., q_{n}[itex]\in[/itex]Nwith q_{1}<q_{2}<...<q_{n}.

My professor suggests using the greedy algorithm but I don't understand how that would help the proof.

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# Proof with rationals and irrationals

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