# Relation vs function

1. Jun 7, 2013

### thedy

Hi,I hope my question will be clear.I need to be explained me one problem.That is:
Can be expressed physical law,for example average speed like relation,but not like a function?Or speed can be only the function?I mean,why we use functions to describe physical phenomena?Is possible to describe every phenomenon with function and also by relation?For example a2 + b2 = c2 is relation,but can be it converted like a function?
I know,that my question is strange,but I m trying to understand,why we use function,and if the function is one of many possible ways to describe a nature.
Thanks

2. Jun 7, 2013

### mathman

The question is confusing. Are you concerned with a mathematical distinction between relation and function or some physics question?

In mathematics, a function is a special case of a relation. Examples: y=f(x) describes a function, g(x,y)=0 is a relation.

3. Jun 7, 2013

### HallsofIvy

Staff Emeritus
Physical quantities have the property that "if all conditions are set exactly the same, then the result is the same". That implies that physical quantities will always be functions of their conditions.

4. Jun 10, 2013

### thedy

Thanks,I give an example.v=s/t...This is a function.But does exist any relation between position and time and velocity,which is not a function?I mean,why all physical laws are functions?Why cannot be physical laws converted to somethin else,which is not function?
Thanks

5. Jun 11, 2013

### Vorde

Well what else do you want?

I can say for constant velocity that Velocity is proportional to distance traveled and inversely proportionally to time elapsed.....but I'm really saying the exact same thing as $V=\frac{s}{t}$; just in a different way.

6. Jun 11, 2013

### Stephen Tashi

If we have data of the form (v,s,t) for an object, the variable t is not a function of (v,s) if the object returns to the same position s with the same velocity v several times. (Such would be the case in periodic motion.)

Not all physical laws are functions of every variable involved in them. In most physical laws, at least some variables are functions of the rest. I think this is just a sociological phenomena. People find formulas that make definite predictions are useful. Formulas that make definite predictions are functions. People call formulas that they find useful "physical laws".

If you want to find a non-sociological reason why most "physical laws" are functions, you have to state a non-sociological definition of "physical law". What makes a particular (true) fact a "physical law" besides people deciding to call it a "physical law"?

7. Jun 30, 2013

### thedy

Hi,I was reading this thread once again to make a better image,what you mentioned.And I have one more question.I do not know,if it is good understandable question,but I am wondering,what is the real difference between equation and function.I give an example:pV=nRT is equation.But it is not a function,Why?And then if i divide by volume this equation I get p=nRT/V.And this is a function now.But actually neither in form of equation nor in form of function,we have not higher or lower quantity of information?Why am I asking that?Because in another website was mentioned that physical laws are mostly in form of equation,like this Vp=nRT.But if I arrange this equation to the form p=nRT/V it is still physical law,state equation.
So my major question is,what is difference between equation and function in context of physical law and if law are expressed like equation,why is it so,and if like function,why is it so too.....I do not need exact answers which are on high level,but I just want to make a first step to better understand,how these stuffs work.How physical law works.....I am reading The character of physical law,but if you have any other tip of good book,feel free to mention it....
Thanks a lot....

8. Jun 30, 2013

### mathman

pV = nRT is a relation. To consider it a function define which variable (p,V,n,T) is the dependent variable, then change the equation into a form "dependent variable" = function(everything else). It is still an equation, but it is now in function form.

I have a feeling you are overthinking.