What Does the Dot Mean in a Function Like f(x,·,·)?

[PhDorBust]

When you see something like f(x,·,·), how are you supposed to interpret it?

Sorry, I can't give example, the only places I've seen have been using it informally.

I read,
http://www.reddit.com/r/math/comments/995dl/ask_math_reddit_what_does_the_dot_in_this/
, but can't find a definitive answer.

 

[mathman]

In the example you give f(x,.,.), the dependence on x is of interest, keeping in mind that f is a function of 3 variables.

 

[PhDorBust]

In the example you give f(x,.,.), the dependence on x is of interest, keeping in mind that f is a function of 3 variables.

So you could substitute arbitrary values for the other arguments with no effect?

Would this be proper (albeit useless) example of usage?
Let function f map R x R to R be defined as f(x,·) = x + 4.

I've always been used to seeing,
Let y be in R. Let function f map R x R to R be defined as f(x,y) = x + 4.

 

[AlephZero]

The real value of the notation is when you don't care at all what sort of object the "dot" represents.

In elementary algebra, you use variables like "x" to mean "any object of some type" - for example "any real number".

If you want to prove a general theorem in mathematical logic about "all possible functions with 3 arguments, regardless of what the functions actually do or what types of arguments they have", then you need notations to represent ideas like "a general example of such a function", or "any possible values of the first argument of such a function".

That is one use for notations like f(.,.,.) and the "x" part of f(x,.,.).