Show that the axiom of completeness is equivalent to the least upper bound property. In class we define the numbers to be an Archimedean ordered field satisfying the axiom of completeness and using these assumptions we proved the least upper property. Here instead define the real numbers as an Archimedean ordered field satisfying the least upper bound property and then prove that every Cauchy sequence converges.

42 0

Get full Expert solution in seconds

$1.97 ONLY

Unlock Answer

EXPERT ANSWER

Leave a Comment

Your email address will not be published. Required fields are marked *