# 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.

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