Today, while reviewing my notes on the complete ordered field of real numbers, I came across this problem which, although seemingly simple, gave me quite a headache for several hours. I hadn't seen anything like it in textbooks. Normally, we only encounter simpler problems and don't have the opportunity to explore them in depth. But that's what someone who studies mathematics should do, haha.
I apologize for the translation of the problem, which was done with a translator, and perhaps also for the solution.
Has anyone here ever encountered a similar problem?
