Note that . So, there exists rational , such that ... And now think how to obtain second rational
I am stuck with this problem
Show that for real functions and such that , there exists rationals and such that and
Would using the Archimedean principle help?
Let and .
By the Archimedean principle, there exists such that
Is this in the right direction?
Thanks in advance
"Show that for real functions and such that , there exists rationals and such that and "
let A =lubf, B=lubg
If A and B are rational and belong to f and g respectiveley, you are finished.
Otherwise you can pick rational numbers r and s greater than A and B respectiveley and arbitrarily close so that r+s < x