A real number is a number that can be used to measure a continuous one-dimensional quantity
- distance
- duration
- temperature, etc.
Every real number can be represented by an infinite decimal expansion.
A real number is any point on a line where the points corresponding to integers are equally spaced
$$(...,-2,-1,0,1,2,...)$$
Real numbers include rational numbers, e.g. -17 or 3/5
And irrational numbers, e.g. $$\sqrt 2$$
The real numbers form an ordered field. The methods of elementary arithetic apply to them.