i need help to demonstrate the next proposition using the definition you are giving me:
A space $(X, d)$ is chained if for all $\epsilon> 0$ and each pair of points $x, y \in X$ there exist $x_{0}, ...., x_{n} \in X$ such that $x_{0}= x, x_{n}= y$ and $d (x_{i}, x_{i + 1}) <\epsilon$ for each $i <n$. Show that if $X$ is connected, then $X$ is chained.
I have a clear idea of how the demonstration is and i see it drawing pictures, but i don’t know how to write it, i would appreciate your help very much please
