is the set of all real numbers is open set?

Question

anonymous · Answer

or closed?

anonymous · Answer

@KingGeorge please help

anonymous · Answer

(-inf, +inf)

kinggeorge · Answer

I think it's usually considered both open and closed since it can be expressed as $$(-\infty, \infty)$$or $$[-\infty, \infty]$$

anonymous · Answer

No, it is recommended to use open set.. because it is going on in both infinite directions.

kinggeorge · Answer

I am rather positive it is both open and closed. A clopen set if you will. Most teachers in High school will use the notation for an open set, but at more advanced levels (such as Real Analysis), it's considered to be clopen.

anonymous · Answer

thanks @KingGeorge

kinggeorge · Answer

You're welcome.

anonymous · Answer

"whenever a space is made up of a finite number of disjoint connected components in this way, the components will be clopen." http://en.wikipedia.org/wiki/Clopen_set so the set of all real numbers is not finite set of all disjoints or is it @KingGeorge

kinggeorge · Answer

No, the real numbers could not be constructed like that.

kinggeorge · Answer

To say it more clearly, you are correct. The set of all real numbers is not a finite set of all disjoint sets. (mostly because it's not finite)