Q: Proof of a continuous function? I would like to know how tho prove or disprove the following:
Prove the following statement:
Every continuous function $f:[a,b] \mapsto \mathbb{R}$ (with $a < b$) is (from above) bounded.
I have to use the opposite position of that statement by using the Weierstrass Interval technique for an appropriate sequence.
I have no idea where to begin and to end...Thanks in advance for your suggestions.

A: Suppose $f$ unbounded.
For $n=1$, we have $x_1$ s.t. $f(x_1)>1$.
For $n=2$, we have $x_2$ s.t. $f(x_2)>2$.
...
For each $n$, we have $x_n$ s.t. $f(x_n)>n$.
Try again from here.
