Mathematics Conventions and Rationale

In summary, the rationale behind mathematics conventions, such as the order of operations, is a topic of debate among mathematicians. Some argue that frequency of occurrence plays a role, while others suggest it is the position of the operator. However, ultimately, these conventions are widely accepted by the mathematical community in order to express operations without ambiguity. While some may find them unreasonable or confusing, they are still necessary in order to maintain consistency and avoid variations in mathematical expressions. The reasoning behind these conventions may not always be clear, but they serve their purpose in allowing for efficient and clear communication in mathematical equations.
  • #1
Qu3ry
6
0
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!
 
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  • #2
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?
 
  • #3
Mentallic said:
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.
 
  • #4
Mentallic said:
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?
 
  • #5
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.
 
  • #6
n.karthick said:
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."
 
  • #7
Qu3ry said:
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.
 
  • #8
n.karthick said:
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.
 
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1. What are some common conventions used in mathematical notation?

Some common conventions in mathematical notation include using symbols like +, -, x, / for basic operations, using parentheses to indicate order of operations, and using subscripts and superscripts to indicate indices and exponents.

2. Why are mathematical conventions important?

Mathematical conventions are important because they provide a standardized way of communicating mathematical ideas and operations. This allows for clear and consistent understanding among mathematicians and scientists.

3. What is the rationale behind the order of operations in mathematics?

The order of operations in mathematics follows the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order is based on the concept of simplifying expressions by dealing with parentheses and exponents first, followed by multiplication and division, and finally addition and subtraction.

4. How are mathematical conventions used in problem-solving?

Mathematical conventions are used in problem-solving to ensure that the correct operations and order of operations are followed. They also allow for clear communication of solutions and make it easier to check for errors.

5. Is it important to follow mathematical conventions in all situations?

Yes, it is important to follow mathematical conventions in all situations, especially in academic and scientific settings. This ensures that mathematical ideas and solutions are accurately and consistently communicated and understood by others.

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