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Mapping a: S -> T be so that any x ε S has one and only one y &#

  1. Mar 29, 2009 #1
    mapping a: S --> T be so that any x ε S has one and only one y &#

    What makes it necessary for any mapping a: S --> T be so that any x ε S has one and only one y ε T?
     
  2. jcsd
  3. Mar 29, 2009 #2
    Re: Mappings

    That's the defining property of a being a function from S to T.
     
  4. Mar 29, 2009 #3
    Re: Mappings

    So it is necessary only by definition?
     
  5. Mar 29, 2009 #4
    Re: Mappings

    It is not necessary at all. One can talk about mappings that are not functions as well. What is the context of this question?
     
  6. Apr 1, 2009 #5
    Re: Mappings

    I see...what I was referring to were particular types of mappings (functions), right?
     
  7. Apr 1, 2009 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Mappings

    It might help if you told us exactly what you mean by "S" and "T"!

    If you are referring to any sets S and T and by "mapping" you specifically meant "function", then yes, that is true simply because of the definition of "function".
     
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