Used by Cantor in lieu of Dedekind cuts for a constructive definition of the reals, they are not necessarily convergent, but their convergence is a necessary condition of completeness.  
Used by Cantor in lieu of Dedekind cuts for a constructive definition of the reals, they are not necessarily convergent, but their convergence is a necessary condition of completeness.  Any convergent sequence in a metric space must be of this type.  Named for a French Mathematician, FTP, identify these sequences such that for any epsilon greater than 0, two members of the sequence may be found which are separated by a distance less than epsilon.
Used by Cantor in lieu of Dedekind cuts for a constructive definition of the reals, they are not necessarily convergent, but their convergence is a necessary condition of completeness.  
Cauchy sequence