Associativity of addition

Statement

For all natural numbers $a$, $b$ and $c$, $(a + b) + c = a + (b + c)$. Here $+$ is the addition of natural numbers.

Remarks

The proof from the recursive definition of addition uses induction on $c$. Because of this law, we can write $a + b + c$ without parentheses. Multiplication of natural numbers is also associative.

Explanations

L1 human

When you add three numbers, you can add the first two first or the last two first. For example, $(2 + 3) + 4 = 5 + 4 = 9$ and $2 + (3 + 4) = 2 + 7 = 9$.