Show that every polytope is bounded

Question

The definition of polytope is the convex hull of a finite set. Thus: $$ \parallel\sum_j\lambda _j x_j\parallel\le\sum_j\lambda_j\parallel x_j\parallel\le\sum_j\lambda_j\max_j \parallel x_j\parallel=M\sum_j\lambda_j=M $$ where $M=\max_j \parallel x_j\parallel$

And how can I conclude from above that every polytope is bounded?

Answer 1

It looks correct. And it seems to me that you proved your assertion. You assumed $M = \max_{1 \le i \le m} \|x_i\|$, of course.