Hi,

i need to prove or disprove the following:

thanks in advanced!

*edit:

both sets are bounded from above.

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- Jan 21st 2013, 05:48 AMStormeyprove or disprove: sup of two sets
Hi,

i need to prove or disprove the following:

thanks in advanced!

*edit:

both sets are bounded from above. - Jan 21st 2013, 06:10 AMemakarovRe: prove or disprove: sup of two sets
Prove (1) and (2) .

For (1), show that is an upper bound of .

For (2), use the fact that and imply . - Jan 21st 2013, 08:53 AMjohngRe: prove or disprove: sup of two sets
I've found the following to be useful:

supremums of larger sets are larger and infimums of larger sets are smaller

Formally, (assuming the sets are bounded):

1. If then

2. If then

Proof of 1 - Let . Let , then and so ; i.e. is an upper bound of . So . The proof for infs is exactly similar.

For your original question, since , , and similarly for B. - Jan 21st 2013, 10:06 AMStormeyRe: prove or disprove: sup of two sets
Thanks guys.