\left( {\forall \varepsilon > 0} \right)\left( {\exists n_0 \in {\bf {\rm N}}} \right)\left( {\forall n \ge n_0 } \right)\left( {\forall x \in \left[ {a,b} \right]} \right)\left( {\left| {f_n \left( x \right) - f\left( x \right)} \right| < \varepsilon } \right)