Closed Infinite intervals Text pasted from Thomas Finney Calculus book here: 

"Infinite intervals are closed if they contain a finite endpoint, and open otherwise.  The entire real line  is an infinite interval that is both open and closed."

Can anyone please explain in simple words the above mentioned two statements?
I am applied maths student so I will not understand anything from pure maths.
 A: An infinite interval has one of these forms:


*

*$(-\infty,\infty)$, which is both open and closed.

*$(a,\infty)$ or $(-\infty,b)$, which are open.

*$[a,\infty)$ or $(-\infty,b]$, which are closed.

A: I think a better (and perhaps more correct) statement is the following: an infinite interval is closed if and only if it contains all of its endpoints.  Conversely, an infinite interval is open if and only if it does not contain any endpoints.
Note that these two statements are not negations of one another, as exemplified by the infinite interval $( -\infty , +\infty ) = \mathbb{R}$.  This interval has no endpoints, and so it does not contain any endpoints, and therefore it is open.  Also, since it has no endpoints, it vacuously contains all of them, and therefore it is closed.
There are only 5 different kinds of infinite intervals:


*

*$(a , +\infty)$;

*$[a , +\infty)$;

*$(-\infty,a)$;

*$(-\infty,a]$; and

*$(-\infty , +\infty)$.


We can then easily check whether they are open or closed (or both!).
