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Need help

  1. Sep 28, 2008 #1
    Find a set A (subset of R,set of real numbers) and an element a of R
    such that there is no bijecton from a+A(we add a to the set A)to A.

    I can't find a good example. Can someone help
    Are we done if we choose the empty set? (And is the empty set a subset of R?)

    Thank you
     
  2. jcsd
  3. Sep 28, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    ?? Any finite set will do. Take A= {1, 2, 3} and a= 0. Then A has 3 members while A+ a has 4. There cannot be a bijection from one to the other.

    Yes, the empty set is a subset of R (it is a subset of any set). Choosing A= {} and a any real number so that A+ a= {a} will also work.
     
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