Classify the number as a member of one or more of the follow

Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, and the irrational numbers.

0.123112311123...

Solution

it cannot be integer and natural number as it is in decimal form. neither it is a rational number because the decimal expression is non-ending and non-repeating. furthermore it can not be written in p/q form where p and q are integers and q is not equal to 0.

the number is a irrational number, as the decimal expression is non-repeating and non-ending.