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Rotation function

  1. Sep 24, 2012 #1

    dpa

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    Hi all,

    Q. A function takes (x,y) and gives (y,x). Is this function injective?

    For any function to be injective, f(x,y)=f(x',y')=>(x,y)=(x',y').
    But here, I get,
    (y,x)=(y',x')
    How can I show the function is injective? It appears to be one.

    Thank You.
     
  2. jcsd
  3. Sep 24, 2012 #2

    LCKurtz

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    Right so far. Can you conclude (x,y) = (x',y') from that?
     
  4. Sep 24, 2012 #3

    dpa

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    the ordered pairs are equal means that we can write y=y' and x=x' which in tern mean that
    (x,y)=(x',y')

    Is this fine.

    Thank You.
     
  5. Sep 24, 2012 #4

    LCKurtz

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    Yes, that's all there is to it.
     
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