Simple Supremum Question

1. Seacow1988

9
If S=sup {Sn: n>N}, is it true that kS= sup{kSn: n>N} where k is any scalar?

Thanks!

2. Seacow1988

9
Woops. I meant k is any nonnegative scalar.

Thanks!

3. micromass

19,369
Staff Emeritus
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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