Some binary operations[1] have something called “the associative property… which means that rearranging the parentheses in an expression will not change the result.”
To elaborate, let “*” be a binary operation[1]. The operation “*” is associative when acting on a specific set[2] S only if the following statement is always true: (x ∗ y) ∗ z = x ∗ (y ∗ z) for all x, y, z in S
Note: associativity means something different in propositional logic, and associativity is not the same thing as commutativity[3].
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Source of quotes and information: “Associative property,” Wikipedia, retrieved 10/10/2020. Bold added to quote for emphasis.
- [1] See “What is the Gist of a “Binary Operation”?“
- [2] See “What is the Gist of a “Set” (Mathematics)?“
- [3] See “What is the Gist of “Commutativity” (Mathematics)?“
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
