Natural numbers are closed under addition.
Step 1: What are natural numbers?
Natural numbers are counting numbers: 1, 2, 3, 4, ... (some books also include 0).
Step 2: What does "closed under addition" mean?
If we add two numbers from the set, the answer should also be in the same set.
Step 3: Try a few examples.
\(2 + 3 = 5\) (and 5 is a natural number)
\(10 + 1 = 11\) (11 is a natural number)
\(25 + 40 = 65\) (65 is a natural number)
Step 4: Write it in math form.
Let \(a\) be a natural number: \(a \in \mathbb{N}\).
Let \(b\) be a natural number: \(b \in \mathbb{N}\).
Then their sum is also a natural number: \(a + b \in \mathbb{N}\).
Step 5: Conclusion.
Whenever we add two natural numbers, we get another natural number. So, natural numbers are closed under addition.