Natural Numbers


Natural Numbers are defined as the set of numbers which lies between one and infinity including one. It can be considered under the set of real numbers as real numbers is a super set of all types of numbers. Thus natural numbers definition can also be given as the set of positive integers as it does not contains any fractional unit or fractional value and contains all positive values.

Natural number can be used for the purpose of counting as number of things can never be negative existing in real world. For instance if we need to count the number of students in a given class, then can they ever be negative?
No, they can never be negative as persons can be one or more than one but it can never go in negative terms. Thus, only positive values are considered and therefore natural numbers can be considered for counting of any places, things or persons and other things which exists in real world.

If there exist any property which is possessed by zero or by the successors of natural number then that property will be satisfied by all other natural numbers. Every natural number has a successor, suppose a natural number denoted by n then its successor denoted by s(n) where s(n) will be equals to s + 1.

In its set there does not exist any element whose successor is zero as it does not involves the negative numbers. Distinct or different natural numbers have different successors, if 'a' is not equals to 'b' then successor of 'a' cannot be equals to the successor of 'b' as every natural number can have only one successor and only one predecessor. Therefore we can say that if two numbers are distinct then their successors will also be different. All type of mathematical operations can be performed over it like addition, subtraction, multiplication, division, power function and others.  

Math Topics