Is $f_n(x)= \frac{x}{n}$  is uniformly   convergent on $\mathbb{R}$ ?  My attempt : i think yes, take $f(x) = \lim_{n\rightarrow \infty}f_n(x) =0$ because  $\sup | f_n(x) - f(x) |= \sup\{\frac{1}{n}\}= 0$  Is its true ?
Let $f_n(x) : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $\dfrac{x}{n}$. Is $f_n$ uniformly convergent?   With "$(a_n)$ is limited and $(b_n)$ converges to 0 $\Rightarrow (a_nb_n)$ converges also to 0" i would guess that $x\cdot \dfrac{1}{n}$ converges uniformly but $x$ is not limited in this case. So does ist converge uniformly or not?
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