Let the function f (x) be defined on the number set X. it is proved that the necessary and sufficient condition for the function f (x) to be bounded on X is that it has both upper and lower bounds on X Thank you very much for the concrete proof process given by the great God~

Let the function f (x) be defined on the number set X. it is proved that the necessary and sufficient condition for the function f (x) to be bounded on X is that it has both upper and lower bounds on X Thank you very much for the concrete proof process given by the great God~

prove:
1. Let f (x) be bounded on X, then there exists m > 0 such that: | f (x)|