Why do we call function a Rule

[SHASHWAT PRATAP SING]

Let's take an example -
f: N-->N
f(x)= 2x
This is called the Rule of the Function.
The rule of the function tells us the relationship between the elements (x,f(x))of the ordered pairs in the Function Set. So, if the rule tells us the relationship then why do we call f(x)= 2x as the rule of the function.
Please help me...

 

[fresh_42]

What does rule mean to you? $f(x)=2x$ is a rule because it tells you how to find the function value given the input value. Law would be conflicting physics and jurisprudence.

 

[Mark44]

Let's take an example -
f: N-->N
f(x)= 2x

This part, f: N-->N, tells you that the function (named f here) pairs an input value from set N with an output value also from set N. By the way, N usually means the natural numbers, 0, 1, 2, 3, and so on.
This part, f(x)= 2x, tells you the rule, or formula -- how to get an output value from a given input value.

So f(3) is evaluated as 2*3, or 6. Similarly, f(5) = 2*5 = 10, and so on.

 

[fresh_42]

So, if the rule tells us the relationship then why do we call f(x)= 2x as the rule of the function.
Please help me...

You spend way too much time on words. If this is so important to you, try to study Wittgenstein. You have the third thread on basically the same issue, and all contain the same answers. If they still do not satisfy you, then you should tell us what would! You can approach this question by pure logic (cp. relations and functions), mathematically (nobody cares the nuances of speech as long as the definitions are clear; and rule is no mathematical term), or philosophically (cp.Wittgenstein and analytic philosophy of language).

From a logical perspective: note that rule is not really defined. It is common language.
From a mathematical perspective: you are wasting your time.
From a philosophical perspective: Wittgenstein is the first address, but I will lead you away from mathematics.

Edit: If English isn't your native language and you are concerned about its correct usage, then I may quote what a mathematician once told me: "Scientific language is broken English." That means, as long as everybody knows what you are talking about, as long you won't have to bother little mistakes.

 

[SHASHWAT PRATAP SING]

You spend way too much time on words. If this is so important to you, try to study Wittgenstein. You have the third thread on basically the same issue, and all contain the same answers. If they still do not satisfy you, then you should tell us what would! You can approach this question by pure logic (cp. relations and functions), mathematically (nobody cares the nuances of speech as long as the definitions are clear; and rule is no mathematical term), or philosophically (cp.Wittgenstein and analytic philosophy of language).

From a logical perspective: note that rule is not really defined. It is common language.
From a mathematical perspective: you are wasting your time.
From a philosophical perspective: Wittgenstein is the first address, but I will lead you away from mathematics.

Edit: If English isn't your native language and you are concerned about its correct usage, then I may quote what a mathematician once told me: "Scientific language is broken English." That means, as long as everybody knows what you are talking about, as long you won't have to bother little mistakes.

I am sorry fresh_42,
But Thankyou for your Help.

 

[SHASHWAT PRATAP SING]

This part, f: N-->N, tells you that the function (named f here) pairs an input value from set N with an output value also from set N. By the way, N usually means the natural numbers, 0, 1, 2, 3, and so on.
This part, f(x)= 2x, tells you the rule, or formula -- how to get an output value from a given input value.

So f(3) is evaluated as 2*3, or 6. Similarly, f(5) = 2*5 = 10, and so on.

Thankyou Mark44 for helping.

 

[fresh_42]

I am sorry fresh_42,
But Thankyou for your Help.

You do not have to apologize. We merely want you to help and proceed. This sometimes means to sound hard. It is fairly simple: a function has only one output value per input value, which is it's definition and distinguishes it from relations in general. Now you have to tell how the mechanism is to find the output value: I just called it mechanism, others call it rule or just function, and the correct word is: definition of the function.

Better draw some examples and decide e.g. why squaring is a function, but its inverse relation is not.

 

[SHASHWAT PRATAP SING]

You do not have to apologize. We merely want you to help and proceed. This sometimes means to sound hard. It is fairly simple: a function has only one output value per input value, which is it's definition and distinguishes it from relations in general. Now you have to tell how the mechanism is to find the output value: I just called it mechanism, others call it rule or just function, and the correct word is: definition of the function.

Better draw some examples and decide e.g. why squaring is a function, but its inverse relation is not.

fresh_42 you have really helped me a lot . That's why I don't hesitate to ask questions even if it's small.Thankyou.