0

The extended real number line is sometimes written as $\mathbb{R} \cup \{+\infty\} \cup \{-\infty\}$.

In ZFC, this would imply that $+\infty$ is some set. In other words, the string $+\infty$ is an identifier for a particular set.

So... which set is this? Or this this technically an abuse of notation?

extremeaxe5
  • 1,110
  • 3
    it doesn't refer to any particular set, just any set that isn't already an element of $\mathbb{R}$ – user363464 Jun 05 '18 at 04:17
  • 1
    For the purpose of compactification you may use any object that is not a real number, take $+\infty={\mathbb R_+}$ for example. – Michael Hoppe Jun 05 '18 at 05:42
  • @user363464 since you got here first, I think you should get to expand your comment into an answer so that the question is no longer unanswered. – Mark S. Jun 09 '18 at 14:14
  • @MichaelHoppe Since you got here second and the other user hasn't, I think you should expand your comment into an answer so that the question is no longer unanswered. – Mark S. Jan 02 '20 at 18:34

1 Answers1

0

For the purpose of compactification you may use any object that is not a real number, take $+\infty=\{\mathbb R_+\}$ for example.

Michael Hoppe
  • 18,103
  • 3
  • 32
  • 49