How do you construct the set of real numbers from integers?

The completion is unique. It should have said "the" not "a".

>The completion is unique.
The metric is not unique. It should have said "a" not "the".

>The completion is unique.
up to isometry

>construct

Why do you need to?

therefore unique

Continued fraction representation

By drawing a line and imagining reasonable things about it.

t. geometer

>constructible numbers

even simple lines can be unreasonable... this was really good N*

youtube.com/watch?v=BBp0bEczCNg