## ABSTRACT

The study of the calculus and its many applications depends crucially on the properties of real numbers. The set of all real numbers is often represented

symbolically by writing either R or R. If x is a real number this is often

shown by writing x R or x /R. Here the symbol / is to be read ‘belongs to’. The formal mathematical name for this symbol is the set membership relation

symbol. There are three different types of real numbers:

1 Positive integers or natural numbers 1, 2, 3, . . . 2 Rational numbers (fractions) of the form p /q with p, q integers with no

common factor, such as 1/3, 27/5, /5/16, . . . 3 Irrational numbers or numbers such as 2 which cannot be expressed as a

rational number.