Es sei a ∈ R ≥ 0 {\displaystyle {}a\in \mathbb {R} _{\geq 0}} , k ∈ N {\displaystyle {}k\in \mathbb {N} } , M = { x ∈ R ≥ 0 ∣ x k ≤ a } {\displaystyle {}M={\left\{x\in \mathbb {R} _{\geq 0}\mid x^{k}\leq a\right\}}} und s = sup ( M ) {\displaystyle {}s={\operatorname {sup} \,(M)}} . Zeige s k = a {\displaystyle {}s^{k}=a} .
