Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What does unique mean?

  1. Oct 24, 2007 #1
    What does "unique" mean?

    I ran into a trivial exercise. If a function f is bijective, show that it has an inverse. That's easy. But then, the question goes: if f has an inverse, show that it is unique.

    I'm not really sure what is meant by "unique." I would assume it is has to do with the function's one-to-one correspondence. That each element in the function is taken cared of (mapped) one at a time. Is this a good analogy? This is not homework by the way.
     
  2. jcsd
  3. Oct 24, 2007 #2
    It means there is only one inverse. In other words if a function, f, has inverses g and h, then g=h, and there is really only one inverse.
     
  4. Oct 25, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    And, of course, "g= h" mean g(x)= h(x) for every x in the range of f.
     
  5. Oct 25, 2007 #4
    That makes sense, thanks.
     
  6. Oct 25, 2007 #5
    x is unique means, there is one and only one thing that x is.

    'The' in the particular, in the singular, is the meaning of 'unique'.

    The definite article 'the' refers to that one and only x.

    The x such that Fx, is that (unique) x which satisfies Fx.

    That there is only one x which satisfies Fx is defined:
    EyAx(x=y <-> Fx).

    The unique x which is F has the property G, means, EyAx((x=y <-> Fx) & Gy).
     
  7. Oct 25, 2007 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, I'm glad we got that clarified!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What does unique mean?
  1. What does Ept mean? (Replies: 1)

  2. What does "det" mean? (Replies: 6)

Loading...