Let-n-2-for-x-0-1-let-consider-A-x-u-R-x-lt-u-n-1-Prove-that-if-a-b-0-1-a-b-A-a-A-b-2-Deduce-x-infA-x-n-

Question Number 81157 by ~blr237~ last updated on 09/Feb/20

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}