Show that an increasing sequence is convergent if it has a convergent subsequence.
The Attempt at a Solution
Suppose xjn is a subsequence of xn and xjn→x.
Therefore [itex]\exists[/itex]N such that jn>N implies |xjn-x|<[itex]\epsilon[/itex]
It follows that n>jn>N implies |xn-x|<[itex]\epsilon[/itex]
The solution that I've been given is much more complicated I'm just wondering whether my simpler solution is also correct.