Associative Law of Addition

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Theorem

On all the number systems:

natural numbers $\N$
integers $\Z$
rational numbers $\Q$
real numbers $\R$
complex numbers $\C$

the operation of addition is associative:

$a + \paren {b + c} = \paren {a + b} + c$


Proof

This is demonstrated in these pages:

Natural Number Addition is Associative
Integer Addition is Associative
Rational Addition is Associative
Real Addition is Associative
Complex Addition is Associative

$\blacksquare$


Sources