Question

how to prove that rational number is order complete.​

Answer 1

The real numbers are complete in the sense that every set of reals which is bounded above has a least upper bound and every set bounded below has a greatest lower bound. The rationals do not have this property because there is a “gap” at every irrational number.

Answer 2

Step-by-step explanation:

There are several ways you can prove this. A rigorous way you can do it is by first proving that a complete ordered field is closed under taking roots of positive elements.

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