What would happen if we changed the quntifiers in a continuity of a fu

The definition of a continuous function at a point ##x_0## is: $\forall \epsilon >0 \exists \delta >0 \forall x(|x-x_0|<\delta \rightarrow |f(x)-f(x_0)|<\epsilon)$ What would happen if we change it to another defintion as: ##\exists \epsilon >0 \forall \delta>0 \forall x(|x-x_0|<\delta... Read more