Someone took a lot of time and did a real number on him with a knife.
A real number is a class (a, say) of rational numbers which satisfies the condition that it is the same as the class of those rationals each of which precedes at least one member of a.
Accordingly this class is a real number; it will be called the real number 2 R .
Note that the class of rationals less than or equal tò 2r is not a real number.
Similarly, any rational real number is distinct from the corresponding rational number.