# You have seen earlier that the set of all natural numbers is closed under addition (closure property). Is this an axiom or something you can prove?

Closure Property of natural numbers: Let there be two natural numbers be x and y

Then according to closure property of natural numbers under addition

If a is a natural number and b is a natural number then a + b is also a natural number.

Now this is something that can be proved by giving examples.

A natural number is set of whole numbers excluding zero, so all the positive integers are Natural numbers.

And when positive natural number is added to another positive natural number we will have a positive integer only.

Let a = 2 and b = 99

Then, a + b = 101 which is also a natural number

You can take any two natural numbers and repeat the above process, addition of those numbers will always be a natural number.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Goprep Genius Quiz on Direct and Inverse proportions32 mins
Genius Quiz | How, When and Where38 mins
QUIZ | Exponents and PowerFREE Class
Ratio and Percentage34 mins
Champ Quiz | Force, Pressure & Sound29 mins
Fun and Games with Conjunctions46 mins
Cell - Number, Size and Shape40 mins
Motion and Time38 mins
Goprep Genius Quiz | Squares and Square Roots34 mins
Quiz | Powers and Exponennts43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

What is the need of introducing axioms?

Karnataka Board - Mathematics Part I

Let be a segment with C and D between them such that the order of points on the segment is A, C, D, B. Suppose AD = BC. Prove that AC = DB.

Karnataka Board - Mathematics Part I

What are undefined objects in Euclid’s geometry?

Karnataka Board - Mathematics Part I