## A General Formula for a Cauchy Sequence in a Space

Let (X,d) be a space with the trivial metric

Now supposeis a Cauchy sequence in the space. LetThere exists such thatso that

Hence a Cauchy sequence in this space takes the form

Let (X,d) be a space with the trivial metric

Now supposeis a Cauchy sequence in the space. LetThere exists such thatso that

Hence a Cauchy sequence in this space takes the form