Simple Supremum Question

Seacow1988

If S=sup {Sn: n>N}, is it true that kS= sup{kSn: n>N} where k is any scalar?

Thanks!

Seacow1988

Woops. I meant k is any nonnegative scalar.

Thanks!

micromass

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.