0
$\begingroup$

Let $c$ be a positive real number and let $X$ be a bounded from above, non-empty subset of $\mathbb R$. Define set $c \cdot X$ as $$c \cdot X = \{ c \cdot x \bracevert x \in X \} .$$ Prove that $c \cdot X$ is non-empty and bounded from above and that $ \sup (c \cdot X) = c \cdot \sup X $.

$\endgroup$

closed as off-topic by user99914, Davide Giraudo, Claude Leibovici, user91500, Frits Veerman May 16 '17 at 9:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Davide Giraudo, Claude Leibovici, user91500, Frits Veerman
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Where are you stuck? $\endgroup$ – florence May 16 '17 at 8:22
  • $\begingroup$ In fact don't really know how to start. I'm a high school student so it's not really my level of maths. Just started attending extra math lessons and got some exercises to start with. I've read a lot and understood what the question is about, what supremum is etc., but haven't seen many mathematical proofs before and don't really know how it's supposed to look like and be formulated. $\endgroup$ – MrLeatherpants May 16 '17 at 17:36
2
$\begingroup$

Hint. If $c>0$ then $x\leq y$ iff $cx\leq cy$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.