The definition that the function f(x) is bounded on the interval I is that there is a positive number m, so that for any x∈I, |f(x)|≤M is constant. No, no solution is defined as: for any large positive number m, there is always x∈I, which makes | f (x) | > m.

At this time, the existence and representation of x are mostly obtained by solving the inequality | f (x) | > m. For this problem, f(x)= 1/x, I=(0, 1), | f (x) | > m means1/x > m. One condition that we need x is x∈(0, 1). At this time, the value of m can be limited to m > 1, then x < 1/M < 1, as long as x is a number between 0 and 1/M. Another method is to increase the denominator of x and take =1/(m+/kloc.

The final proof process is shown in the figure.