Simple Supremum Question

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

  2. jcsd
  3. Woops. I meant k is any nonnegative scalar.

  4. micromass

    micromass 20,059
    Staff Emeritus
    Science Advisor
    Education Advisor

    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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