Number mapping

Let us consider the number 0.6992797852 with representation as given above. The next number in the computer representation is given by making the smallest change possible to the mantissa, i.e. adding 1 to it, i.e.

> Mantissa1:=convert(101100110000010000000000,decimal,binary);

> Mantissa2:=convert(101100110000010000000001,decimal,binary);

> number1:=evalf(Mantissa1*16^(-6));

> number2:=evalf(Mantissa2*16^(-6));

This shows that the number system as used by a computer is a discrete set of numbers unto which the continuous set of real numbers needs to be mapped.