Mathematics Conventions and Rationale

[Qu3ry]

Have you ever wondered the rationale behind mathematics conventions?

Why multiplication is evaluated before addition, and not the other way around ? Either way would make the expression 3 x 5 + 8 unambiguous.

Some argue that the frequency of occurrence plays a role in the convention, implying multiplication occurs more often than addition. But how do you explain factorials evaluated before addition? It's certainly not more frequent than addition.

Others suggest that it's position of operator that plays a role in such convention, claiming that prefixes or suffixes, such as factorials and exponents, must be evaluated before others. Is that true? How do you evaluate the following expression without parenthesis?

4
Π n+1
n=1

[URL]http://img.mathtex.org/3/36c0f2ddfb8b7ed0fa7f9f5a4cdd126d.png[/URL]

Latex:

\prod_{n=1}^{4}n+1

Where to find an authoritative source of mathematics conventions? Thanks in advance!

 

[Mentallic]

No, I haven't really wondered about it. I mean, there has to be SOME convention so there aren't any variations universally which would create confusion.
But it could just as well be because of frequency. How often do you need to evaluate an exponent of the addition of two numbers, rather than just the one number itself? a+bⁿ versus (a+b)ⁿ.
If it was conventional to do addition first, then how do you express a+bⁿ simply?

 

[Qu3ry]

If it was conventional to do addition first, then how do you express a+bⁿ simply?

Parenthesis.

The order of operation and parenthesis are both means to disambiguate expressions, if any. The order of operation was introduced to lessen the use of parenthesis.

 

[Qu3ry]

But it could just as well be because of frequency. How often do you need to evaluate an exponent of the addition of two numbers, rather than just the one number itself?

Are you implying that the more frequent the operation the lower the precedence (order of operation) ? Isn't that weird?

 

[n.karthick]

When you say it is a convention it means that it is something which is widely accepted by the community and there is no need for any reason or explanation behind that. The mathematical conventions are like that to express mathematical operations without any ambiguity. I think, no need to worry too much about it.

 

[Qu3ry]

When you say it is a convention it means that it is something which is widely accepted by the community and there is no need for any reason or explanation behind that. The mathematical conventions are like that to express mathematical operations without any ambiguity. I think, no need to worry too much about it.

No. I am not worry about it. I am just intellectually curious about it.

If new conventions contradict with existing ones, or they are extremely inconvenient to use, you would complain, saying something like, ''it's unreasonable!".

So, it's false to say "there is no need for any reason or explanation behind that."

 

[n.karthick]

If new conventions contradict with existing ones, or they are extremely inconvenient to use, you would complain, saying something like, ''it's unreasonable!".

So, it's false to say "there is no need for any reason or explanation behind that."

For example, the conventional current direction flowing in a conductor is opposite to the direction of flow of electrons. Though it is unreasonable, it is still in use, and always confuses the beginners (at least it confused me a lot) who learn electricity. We can't do much about conventions and we are forced to accept them.

 

[Qu3ry]

For example, the conventional current direction flowing in a conductor is opposite to the direction of flow of electrons. Though it is unreasonable, it is still in use, and always confuses the beginners (at least it confused me a lot) who learn electricity. We can't do much about conventions and we are forced to accept them.

Yup. What you said are supporting my point, rather than refuting it.

If there is no reason behind it, good or bad, you can't make a value judgment on the convention.

What I am asking is the rationale, not causality, of the convention. Why apples fall? There is no rationale behind it, but there is causality, ie, the law of physics behind it.