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What does it mean for a function to be unique?

  1. Nov 30, 2006 #1
    What does it mean for a function to be unique?
     
  2. jcsd
  3. Nov 30, 2006 #2

    arildno

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    In what context?

    To say that y is a function of x if and onliy if for each choice of x there exist a UNIQUE y corresponding to that x.
    This is part of the DEFINITION of a function in general.

    Having a problem where we say that there exist a unique function as our solution (of for, example a differential equation) is the uniqueness property of our problem.
     
  4. Nov 30, 2006 #3

    matt grime

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    Look in the dictionary....
     
  5. Dec 1, 2006 #4

    HallsofIvy

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    To say that a function, satisfying certain conditions is "unique" means that it is the only function satisfying those conditions.

    For example, there is a unique function, y(x), satisfying y"= -y, y(0)= 0, y(1)= 1. (That unique function is y(x)= sin(x).)
     
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