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Proof about Ordering the Real Numbers

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Given any two real numbers x < y, we can find a rational number q such that
x < q< y.

Hint: you can prove this by using the following statement: for any positive real number x > 0 there exists a positive integer N such that x > 1/N > 0

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** Please see the attachment for the complete solution response **

Given any two real numbers x < y, we can find a rational number q such that x < q< y.
Hint: you can prove this by using the following statement: for any positive real number x > 0 there exists a positive integer N such that x > 1/N > ...

Solution Summary

This solution explains how to provide proof about the ordering of the given real numbers.

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