What is a real number and can you explain why the inequality x<2 or x>1 has every real number as a solution?
1 Answer
Let's handle the second part first:
what values of
Consider two cases:
Case 1:
Case 2:
if
and therefore it must be included
Note that the results would be quite different if the condition had been
One way to think about Real numbers is to think of them as distances, comparable measure of length.
Numbers can be thought of as an expanding collection of sets:

Natural numbers (or Counting numbers): 1, 2, 3, 4, ...

Natural numbers and Zero

Integers: Natural numbers, Zero, and Negative version of Natural numbers ....4, 3, 2, 1, 0, 1, 2, 3, 4, ....

Rational numbers: Integers plus all values that can be expressed as the ratio of two integers (fractions).

Real numbers: Rational numbers plus Irrational numbers where Irrational numbers are values which exist as lengths but can not be expressed as fractions (for example
#sqrt(2)# ). 
Complex numbers: Real numbers plus numbers with components that include
#sqrt(1)# (called Imaginary numbers).