I was watching a video stream a little bit ago and noticed on an equation without context that had the interval $\left[{-\infty, \infty}\right]$. This was preculiar to me as I've never seen the interval for $\mathbb{R}$ expressed this way before, however, I do vaguely remember hearing something about this a long time ago and its use in the construction of certain uncountably infinite sets in axiomatic set theory, but I'm not sure. Is there any use in writing ${-\infty, \infty}$ in a closed interval? If so, what would its use be?

  • $\begingroup$ The extended real number line will be of interest. $\endgroup$ – Irregular User May 10 '16 at 18:52
  • $\begingroup$ @IrregularUser Thanks, that's just what I was looking for! $\endgroup$ – joshumax May 10 '16 at 18:53
  • 1
    $\begingroup$ Hopefully someone can answer the part of your question "If so, what would its use be?"! $\endgroup$ – Irregular User May 10 '16 at 18:54
  • $\begingroup$ The Wikipedia article goes over its uses in measure theory pretty well though $\endgroup$ – joshumax May 10 '16 at 19:04

$[-\infty,+\infty]$ refers to the extended reals. In general, though, $\mathbb{R}=(-\infty,+\infty)$.


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.