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?

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- October 22nd 2009, 10:28 PMamm345Sequences- SupremumIs 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?

- October 23rd 2009, 02:49 AMtonio
- October 23rd 2009, 06:25 AMamm345
Can you please elaborate on that?

- October 23rd 2009, 06:58 AMHallsofIvy
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.