Simple Supremum Question

  • Thread starter Seacow1988
  • Start date
  • #1
If S=sup {Sn: n>N}, is it true that kS= sup{kSn: n>N} where k is any scalar?

Thanks!
 

Answers and Replies

  • #2
Woops. I meant k is any nonnegative scalar.

Thanks!
 
  • #3
22,129
3,297
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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