As part of a problem that I am solving, I am required to postulate a statement concerning $\sup (cA)$ where $c\in\mathbb{R}$ and $c<0$, having just before proved that $\sup (cA) = c\sup(A)$ when $c>0$.
But if we consider the set $A = \{x|x\leq a\}$ where $a\in\mathbb{R}^+$ then by definition $cA = \{cx|x\in A\}$ where $c<0$ but $cA$ is not bounded above and therefore has no supermum, So how can we postulate a general statement where it does not even make sense in this particular case?
PS: I forget to mention this before, but for all sets under consideration, we can only assume that they are bounded above.