how do you prove from the completeness axiom that an increasing sequence an which is bounded above is convergent.
do you start with saying its non-empty and bounded above so there's a least upper bound, say U.
then a(n) is less than or equal to U for all n.
then for all positive epilson there's N s.t
la(n) - Ul < epilson for all n>N
but it seems like i'm fudging it to get epilson into this. i've lost workbook 5, and i think it's from there.
thanks for any help, i just want a rigorous answer.