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The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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what Order of operations is defined as

Q: What Order of operations is defined as?

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That is how the order of operations is defined.

Those are conventions. Many people have gotten accustomed, over the years, to doing operations in a certain order. You can invent your own set of rules, but those would have to be clearly stated to avoid confusion... and it would serve no useful purpose. Having SOME order of operations defined is useful, to avoid having to write parentheses any time you have more than one operation.

[9+4]3

Because if you did operations in an impermissible order, or violated laws of operations, then your solution to the equation is wrong.

If defined, they are inverse operations. However, multiplication and division is a somewhat flawed example because division by 0 is not defined. So, if you have a number x, then x*0 = 0 but 0/0 is not x: it is not defined.

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That is how the order of operations is defined.

It wouldn't be what it is unless if it didn't have to be that way

The number of binary operations that can be defined on a set with 4 elements is 4^(4*4) = 4^16 = 4.294.967.296

Those are conventions. Many people have gotten accustomed, over the years, to doing operations in a certain order. You can invent your own set of rules, but those would have to be clearly stated to avoid confusion... and it would serve no useful purpose. Having SOME order of operations defined is useful, to avoid having to write parentheses any time you have more than one operation.

If you put in parentheses, you can change the order of operations in many cases, as parentheses come before everything in the order of operations.

It means that the calculator can follow the order of operations and do the order of operations for you but, you need to know how to do them on your own too.

[9+4]3

yes

Because if you did operations in an impermissible order, or violated laws of operations, then your solution to the equation is wrong.

If defined, they are inverse operations. However, multiplication and division is a somewhat flawed example because division by 0 is not defined. So, if you have a number x, then x*0 = 0 but 0/0 is not x: it is not defined.

A join and meet are binary operations on the elements of a POSET, or partially ordered set. A join on a set is defined as the supremum with respect to a partial order on the set, provided it exists. A meet on a set is defined either as the unique infimum with respect to the partial order imposed on the set, if the infimum exists.

These are three numbers without any operations defined.