Question

设函数f(x)在数集X有定义,试证：函数f(x)在X上有界的充分必要条件是它在X上既有上界又有下界.

Answer 1

……这个也需要证明?

|f(x)| ≤ M → -M ≤ f(x) ≤ M,所以有界则既有上界又有下界.

A ≤ f(x) ≤ B → |f(x)| ≤ max{|A|,|B|},所以既有上界又有下界则有界.