 Accordingly an additional condition is needed to define a continuum. Cantor supplies this by introducing the concept of a connected set. A point set \(T\) is connected in Cantor’s sense if for any pair of its points \(t, t'\) and any arbitrarily small number \(\varepsilon\) there is a finite sequence of points \(t_1,\) \(t_2,\)…, \(t_n\) of \(T\) for which the distances \([tt_1],\) \([t_1 t_2],\) \([t_2 t_3],\) …, \([t_n t'],\) are all less than \(\varepsilon\). Cantor now defines a continuum to be a perfect connected point set.