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Help with notation

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  1. Nov 19, 2014 #1
    Having trouble understanding some notation:

    x(.) or C(.) (the dot is in fact in the center i.e mid-way vertically in the brackets).

    I have never run into this before? What does it mean if x is a function of "."?
     
  2. jcsd
  3. Nov 19, 2014 #2

    haruspex

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    More context please.
     
  4. Nov 19, 2014 #3
    Apologies, I thought it was something along the lines of f' being the first derivative of the function, and nothing else (to my knowledge).

    And I quote "C(.) is a choice rule (technically a correspondence) that assigns a nonempty set of chosen elements C(β) ⊂ β for every budget set β ∈ B."
     
  5. Nov 19, 2014 #4

    haruspex

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    Seems like it is just a way of saying "C is a function".
     
  6. Nov 19, 2014 #5
    Ok, thanks!
     
  7. Nov 19, 2014 #6
    Someone has mentioned to me that it indicates that a function can only take a single argument . . . without specifying the specific argument?
    Not sure if this is true.
     
  8. Nov 19, 2014 #7
    I got a formal answer:

    f(.) means that we have a univariate (one variable) function.
    The difference between f(x) and f(.) is that that, f(x) denotes a univariate function depending from the specific one-variable x, whilst f(.) denotes an one variable function depending from any one-variable we like.
    We can write, for instance, f(x) or f(y) or f(z) etc
     
  9. Nov 19, 2014 #8

    Ray Vickson

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    Be very careful about what you regard as a "variable". I have seen functions C(.) whose arguments are n-vectors, so we really have ##C(x_1,x_2, \ldots x_n)##, but with the n arguments bundled together into a single "vector" ##\vec{x} = (x_1,x_2 \ldots,x_n)##. In that sense, C is a function of the single "variable} ##\vec{x}##. I have also seen functions C(.) whose arguments are functions themselves (such things are usually called functionals), so in a sense are functions of infinitely many variables. But, again, these several variables are all bundled together into a single object ##x(.)##, and that is plugged into the formula for C.
     
  10. Nov 22, 2014 #9

    Fredrik

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    The dot notation is often used when you want to define a function from one that's already defined, without coming up with a new function symbol. For example, if ##f:\mathbb R^2\to\mathbb R## and ##y\in\mathbb R##, then ##f(\cdot,y)## denotes the function ##x\mapsto f(x,y)## with domain ##\mathbb R##, i.e. the function ##g:\mathbb R\to\mathbb R## such that ##g(x)=f(x,y)## for all ##x\in\mathbb R##. So for all ##x\in\mathbb R##, we have ##f(\cdot,y)(x)=f(x,y)##. The dot is just telling you where to put the "input".
     
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