I've found really good answers for the question from link below.

Any open subset of $\Bbb R$ is a at most countable union of disjoint open intervals. [Collecting Proofs]

But I have a question about how $\mathbb{R}$, which is open subset of $\mathbb{R}$, can be expressed as union of countable collection of disjoint open intervals. In my intuition, it seems not possible.... Thanks for your help.


Open intervals in $\Bbb R$ are allowed to extend to $\infty$, so $(-\infty,\infty)$ is one open interval that is all of $\Bbb R$.

  • $\begingroup$ Oh...so infinite end point is possible. Thank you!! $\endgroup$ – twnzre Dec 25 '19 at 14:47
  • 1
    $\begingroup$ In one sense it is not an end point, because the interval is open. The use of $\infty$ means there is no end point. $\endgroup$ – Ross Millikan Dec 25 '19 at 14:49
  • $\begingroup$ Oh that's right Thanks for correction $\endgroup$ – twnzre Dec 25 '19 at 14:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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