Why the the other supremum sum is bigger

[transgalactic]

i can't understand this part of the solution..

http://img6.imageshack.us/img6/4977/43245163.th.gif

its seems like the same thing

 

[tiny-tim]

i can't understand this part of the solution..

its seems like the same thing

Hi transgalactic!

That's sup(xn + yn) ≤ sup{xn} + sup{yn} …

the sum of two things can't be larger than the sum of their maximum possible values …

but it can be smaller (for example, xn = 0 and yn = 1 for n odd, but xn = 1 and yn = 0 for n even … then sup(xn + yn) = 1, but sup{xn} + sup{yn} = 2)

what's worrying you about that?

 

[transgalactic]

ahh thanks
:)