: Mathématiques: associative property

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associative property

In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: ${\\displaystyle {\egin{aligned}(2+3)+4&=2+(3+4)=9\\,\\\\2\ imes (3\ imes 4)&=(2\ imes 3)\ imes 4=24.\\end{aligned}}}$ Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Associative_property)

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