Which property is $(x + y) + z = x + (y + z)$ $(x+y)+z=x+(y+z)$ ?

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Answer 1 · 2015-06-10T22:35:19

Associativity of addition.

Addition and multiplication are both associative operations:

$(x + y) + z = x + (y + z)$ $(x + y) + z = x + (y + z)$ for all $x$ $x$ , $y$ $y$ and $z$ $z$ .

$(x \cdot y) \cdot z = x \cdot (y \cdot z)$ $(x * y) * z = x * (y * z)$ for all $x$ $x$ , $y$ $y$ and $z$ $z$ .

Notice that subtraction and division are not associative operations:

$(x - y) - z \neq x - (y - z)$ $(x - y) - z != x - (y - z)$ (except when $z = 0$ $z = 0$ )

$(x \div y) \div z \neq x \div (y \div z)$ $(x -: y) -: z != x -: (y -: z)$ (except when $x = 0$ $x = 0$ or $z = 1$ $z = 1$ )

Which property is (x+y)+z=x+(y+z)(x+y)+z=x+(y+z)?