Question

6. Let $S \subset \mathbb{R}$ be a nonempty bounded subset. Given $k \in \mathbb{R}$ define $kS = \{ks : s \in S\}$. Prove the following: (a) If $k > 0$, then $\sup(kS) = k \cdot \sup S$. (b) If $k < 0$, then $\sup(kS) = k \cdot \inf S$.

          6. Let $S \subset \mathbb{R}$ be a nonempty bounded subset. Given $k \in \mathbb{R}$ define $kS = \{ks : s \in S\}$.
Prove the following:
(a) If $k > 0$, then $\sup(kS) = k \cdot \sup S$.
(b) If $k < 0$, then $\sup(kS) = k \cdot \inf S$.

6. Let S ⊂ℝ be a nonempty bounded subset. Given k ∈ℝ define kS = {ks : s ∈ S}.
Prove the following:
(a) If k > 0, then sup(kS) = k ·sup S.
(b) If k < 0, then sup(kS) = k ·inf S.

Added by Lori L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

03/07/2022

Step 1

b) If k < 0, then sup(kS) = inf(S) bounded above. Show more…

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Texts: Please help! Is this statement true? 6. Let SCR be a nonempty bounded subset. Given k ∈ R, define kS = {ks : s ∈ S}. Prove the following: a) If k > 0, then sup(kS) = k * sup(S). b) If k < 0, then sup(kS) = inf(S) bounded above. Prove that if.