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).
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
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.
Because if you did operations in an impermissible order, or violated laws of operations, then your solution to the equation is wrong.
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.
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.
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.
[9+4]3
yes
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.
These are three numbers without any operations defined.
Because if you did operations in an impermissible order, or violated laws of operations, then your solution to the equation is wrong.
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.