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What is an associativity?

What is an associativity? Here are some definitions.

Noun
  1. (algebra) The condition of being associative.
  2. (programming) The property of an operator which determines how it is grouped with operators of the same precedence in the absence of parentheses.
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Examples
Using the associativity shortcut, subtracting or dividing first, can simplify problem solving significantly.
This level of associativity pushes the collaborative possibilities further than ever before by seamlessly integrating into PLM systems.
While this is the content of associativity, for ease of processing associativity is almost always expressed as a symbol-manipulation rule.
It is subjected to certain conditions and, for example, to the rules of commutativity and associativity of addition.
The associativity between master model and derived drawings ensures that any model change is immediately apparent to the employees.
Moreover, the end-to-end concatenation of rigid rods shares structural features such as associativity and commutativity with the mathematical operation of addition.

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