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Which branch of mathematics is this?

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm wondering which branch of mathematics is given in the following paper. What I understand in it is the function set mapping notation (f:X->Y), series and sequence notation, but nothing else. I want to know which branch of mathematics this is to be able to read this paper.


    2. Relevant equations
    Ip6x3.png


    3. The attempt at a solution
    I tried Goolging without any luck.
     
  2. jcsd
  3. Jun 2, 2012 #2
    There isn't really any math content here, it's just definitions on this page. If you don't understand what the symbols mean it would probably be good to ask an economist (is this econ??). All I can say other than that is that set theory or some discrete math might help you with the symbols, but they probably wouldn't help you with whatever it is the author is going to do next.
     
  4. Jun 2, 2012 #3
    It could be economics. Or it could be this kind of a thing. Whatever it is, it surely isn't pure math.
     
  5. Jun 2, 2012 #4
    But what does it mean when there's an infinity exponent of a set "X"? Isn't it mathematics (set theory)?
     
    Last edited: Jun 2, 2012
  6. Jun 2, 2012 #5

    Mark44

    Staff: Mentor

    It's not an exponent. This --
    $$\{x_t\}_{t = 0}^{\infty}$$
    -- is notation for an infinite sequence of numbers, and t is the index, which ranges through all nonnegative integers.

    It's a compact way of writing
    ##\{x_0, x_1, x_2, \cdot \cdot \cdot, x_t, \cdot \cdot \cdot \}##
     
  7. Jun 3, 2012 #6
    I know this notation, which is used to define discrete functions. I was talking about the notation which has an infinity exponent in the range of the function. That is X^∞, with X being the domain set. It's on the second line of the paper.

    And also, does $$U(x_0, x_1, x_2 ... x_n)$$ mean that the function U is an n+1 dimensional function? For example, the same way f(x, y) is a 3 dimensional function?
     
    Last edited: Jun 3, 2012
  8. Jun 3, 2012 #7

    Mark44

    Staff: Mentor

    I didn't notice that X before. What this means is that the domain (not range) of the utility function U is a set of infinite sequences.
    I would not use this terminology. ##U(x_0, x_1, x_2 ... x_n)## is a function of n + 1 variables. f(x, y) is a function of two variables. The graph of U requires n + 2 dimensions; n + 1 dimensions for the domain, and one dimension for the range. Similarly the graph of f requires 3 dimensions; two for the domain and one for the range.

    Keep in mind that U as defined in the paper is a map from the space of infinite sequences to the real numbers. For this reason, the domain is infinite dimensional, and the range is one dimensional.
     
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