what are the set of real numbers greater than 12 or less than four?

Question

Need help understanding number sets.

Answer 1

The Real Number line is shown below.  It extends from - infinity to + infinity.  It includes the integers and all numbers in between (deimals).  The numbers get smaller as you move left and bigger as you move right.  I've labeled every other integer on the number line.  Below, I've shown the set of real numbers that are less than 4 (x<4) and greater than 12 (x>12).  The O symbol denotes that 4 and 12 are not included.  If we had wanted x greater than or equal to 12 (denoted x ≥ 12), we would use a filled in o to show that 12 was included.

 

   -14 -12  -10    -8    -6   -4    -2     0     2     4     6      8    10   12   14   16   18

<--|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|---->

<==============================O                             O=============>

                x < 4                                                                                     x > 12

 

In formal set notation:

 

{x|x∈R,x<4 and x>12}

 

which reads: The set of all x such that ({x|...}) x is a member of the set of real numbers (x∈R) and x is less that 4 (x<4) and x is greater than 12 (x>12).