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I have a question I would like assistance with:

let (v,||.||) be a norm space over ℝ, and let f:v→ℝ be a linear functional.

if f is continuous on 0 (by the metric induced by the norm), prove that there is k>0 such that for each u in v, |f(u)| ≤ k*||u||.

thanks :)