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Simple Supremum Question

by Seacow1988
Tags: supremum
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Seacow1988
#1
Feb17-11, 02:30 PM
P: 9
If S=sup {Sn: n>N}, is it true that kS= sup{kSn: n>N} where k is any scalar?

Thanks!
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Seacow1988
#2
Feb17-11, 02:35 PM
P: 9
Woops. I meant k is any nonnegative scalar.

Thanks!
micromass
#3
Feb17-11, 04:10 PM
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P: 18,330
Yes, I think that this is indeed true for nonnegative scalars k. The proof is not so hard: just show that S is an upper bound and that no lower upper bound exists.


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