Question

Show that any discrete space is complete

Answer 1

Answer:

So in discrete metric space, every Cauchy sequence is constant sequence and that way every Cauchy sequence is convergent sequence. Thus we conclude the discrete metric space is complete.

Answer 2

Answer:

So in discrete metric space, every Cauchy sequence is constant sequence and that way every Cauchy sequence is convergent sequence. Thus we conclude the discrete metric space is complete.