Is it true that for every two sequences{xn} n goes from 1 to infinityand {yn}n goes from 1 to infinity satisfying for every n xn < yn one has
a. sup xn <or=sup yn?
b. sup xn < sup yn?
How do you prove or disprove these?
He gave an example of sequences and with but [tex]sup \{x_n\}= sup \{y_n\}[/itex]
Perhaps a simpler example would be and for all n. for all n but their supremums (in this case they are both non-decreasing sequences so their supremums are just their limits- and both are 0.