Let n≥2 , for x∈[0,1] : let consider A(x)={ u∈R_+ ^∗ \ x<u^n } 1)Prove that if a,b∈[0,1] a≤b ⇔A(a)⊆A(b) 2)Deduce x=[infA(x) ]^n


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Question Number 81157 by ~blr237~ last updated on 09/Feb/20
$Let n≥2 , for x∈[0,1] : let consider A(x)={ u∈R_+ ^∗ \ x<u^n } 1)Prove that if a,b∈[0,1] a≤b ⇔A(a)⊆A(b) 2)Deduce x=[infA(x) ]^n$
$L e t n ⩾ 2, f o r x \in [0, 1] : l e t c o n s i d e r A (x) = {u \in R_{+}^{*} ∖ x < u^{n}}$ $1) P r o v e t h a t i f a, b \in [0, 1] a ⩽ b \Leftrightarrow A (a) \subseteq A (b)$ $2) D e d u c e x = {[i n f A (x)]}^{n}$
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