# Every totally ordered field satisfying archimedean property can be embedded in the real numbers.

I need a reference for the following result:

Theorem: Every totally ordered field satisfying the Archimedean property can be embedded in the real numbers.

There are books that mention this result without any proof or reference. Someone knows any good reference? The more the better.

• That is to say it IS a subset of some construction of the real numbers – Jacob Wakem Nov 2 '16 at 18:39

The basic idea is fairly simple: let $F$ be such a field. Then you observe
• There are no infinitesimals in $F$
• The rationals are dense in $F$