Real Numbers
All the weighing, measuring and calculating that are in commerce and science require the use of the real numbers. To the Mathematician, they are the numbers, both positive and negative, which can be represented by points on the real number line.
(i) = the set of real numbers (ii) 
Ì Ì
Ì
Irrational Numbers
The rational numbers do not 'fill' the number line. There are points on the number line, that represent Ö2 fo example, which do not represent rational numbers, i.e. some real numbers are not rational numbers.
Any real number can be expressed in decimal form, example =1.7;
=0.09;
. In the case of a rational number the decimal expansion will ultimately repeat as for example in the case,
or
. In the case of an irrational number such as Ö2=1.41423... or p=3.14159... no such repetition can occur.
