Can someone explain, please?

Question

So, there's a problem that is telling me write my answer in Interval Notation and it is telling me to do so except for -3 and 3. I am able to get the answer for the two numbers, but there's also a third ordered pair that is the two numbers itself (-3,3) along with a second union symbol. I'm trying to get an answer/reasoning as to why that is so.

Answer 1

You want all numbers from -∞ to ∞ except for the two numbers -3 and 3.  So you will have one interval that goes from -∞ to -3, (-∞,-3); a second interval from -3 to 3, (-3,3); and a third interval from 3 to infinity, (3,∞). 

 

       (-∞,-3)      (-3,3)     (3,∞)    

-∞<-----------o---------o----------> ∞

                   -3           3

 

Now combine them with union symbols (U):

(-∞,-3)U(-3,3)U(3,∞)