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Injection on QxQ

  1. Sep 29, 2013 #1
    I just want to ask.

    For the set {a^2+b^2 , a,b [itex]\in[/itex] Q}. Am i then right in saying that the map:

    f(a^2+b^2)=(lal,lbl) is an injection on QxQ (the absolute values are there to make sure f is well-defined)? And is this how you write a thing like this formally.
     
  2. jcsd
  3. Sep 29, 2013 #2

    Office_Shredder

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    Your function is not well defined - note that a2+b2 is always an element of Q if a and b are, so you are saying f(x) = (|a|,|b|) for any way that I can pick a and b to write x = a2+b2. There are generally going to be multiple ways to write x in this way, for example
    4 = 02 + 22 = 22 + 02,

    so is f(4) supposed to be (2,0) or (0,2)?
     
  4. Sep 30, 2013 #3
    ugh I see I made a mistake:
    What I meant was:
    f(a^2+b^2)=lal+lbl
    now f is injective right?
     
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