# Simple Supremum Question

by Seacow1988
Tags: supremum
 P: 9 If S=sup {Sn: n>N}, is it true that kS= sup{kSn: n>N} where k is any scalar? Thanks!
 P: 9 Woops. I meant k is any nonnegative scalar. Thanks!
 Mentor P: 16,542 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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