If I want to know wither $\displaystyle lim_{n\rightarrow \infty}\ sup_{x\in X} |f_n(x)|$=0 can i say that if for some value of

$\displaystyle y=|f_n(x)|\ \mbox{where}\ x\in X$ we have that

$\displaystyle lim_{n\rightarrow \infty} y>0$ then it is not the case that

$\displaystyle lim_{n\rightarrow \infty}\ sup_{x\in X} |f_n(x)|$=0 as $\displaystyle y\leq sup_{x\in X} |f_n(x)| $

Im struggling to come up with a counter example or anything for this.

thanks for any help