associative property
The grouping of terms within expressions involving addition or multiplication does not change the value. Ex: (a+b) + c = a + (b+c)
Associative property is a property of binary operations, which are operations that involve two elements. The associative property states that when performing an operation involving three or more elements, the order in which the operation is performed does not affect the result. More formally, if * is a binary operation on a set S, then the associative property states that for any three elements a, b, and c in S:
(a * b) * c = a * (b * c)
In other words, the grouping of elements does not matter when performing the operation. For example, addition and multiplication are associative operations. For instance, (2+3)+4 = 2+(3+4) and (23)4 = 2(34) both demonstrate the associative property.
The associative property is important in many areas of mathematics, including algebra, calculus, and set theory. In algebra, the associative property is used to simplify expressions involving multiple operations. In calculus, the associative property is used to group terms in series or sums. In set theory, the associative property is used to define binary operations on sets, such as the intersection and union of sets.
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