Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If we define a metric $d : \mathbb{Z^+} \times \mathbb{Z^+} \to \mathbb{R}$, where $\mathbb{Z^+}$ is the set of positive integers and $\mathbb{R}$ is the set of reals, as follows:

$$d(m,n) := |m^{-1} - n^{-1}|$$

for all $m$, $n \in \mathbb{Z^+}$, then how to prove if this metric space is complete?

share|cite|improve this question
I think you mean $d \colon \mathbf{Z^+}\times \mathbf{Z^+} \to \mathbf{R^+}$. As with your other question, a metric takes pairs of points in a space to a distance. – Ross Millikan Jan 28 '13 at 0:38
Oops sorry! It's the set of positive integers. – Saaqib Mahmuud Jan 28 '13 at 0:40

Hint: What's the limit of $a_n = n$? Is it a positive integer?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.