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Math Help - Tuple definition and iteration of sets

  1. #1
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    Tuple definition and iteration of sets

    Hi,

    I wonder if someone would like to give a tip or two on these topics...so here goes.

    1. I want to define a tuple of three sets where one set can possibly be empty. How can I describe this?

    2. I wonder how to apply a function to all elements of a set.

    3. How can I specify that the legal type of argument to the function 'iterate' is all kind of sets (or eventually a special kind of sets)? That is, how do I specify the type of argument of a function?

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  2. #2
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    1. What do you mean? Do you mean to define <x y z> where any of x, y, or z might be empty?

    This is simple:

    <x y> = {{x} {x y}}

    <x y z> = <<x y> z>

    That any of x, y, or z might be empty is irrelevant.

    2. What do you mean? Given a set S and a function f, it might or might not be the case that S is a subset of the domain of f.

    3. I don't know what function 'iterate' you have in mind.
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  3. #3
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    Quote Originally Posted by MoeBlee View Post
    1. What do you mean? Do you mean to define <x y z> where any of x, y, or z might be empty?

    This is simple:

    <x y> = {{x} {x y}}

    <x y z> = <<x y> z>

    That any of x, y, or z might be empty is irrelevant.

    2. What do you mean? Given a set S and a function f, it might or might not be the case that S is a subset of the domain of f.

    3. I don't know what function 'iterate' you have in mind.
    Thanks for taking the time to give a reply to this. I see that my initial description was kinda confusing. Regarding 3.: obviously the types of arguments a function can be applied on is specified explicitly like f : X x Y -> Z. That was basically what I was after.
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