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Math Help - Function question

  1. #1
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    Function question

    Give an example of a function f and a set A such that  f \cap A^2 \neq f \upharpoonright A

    Any ideas?
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  2. #2
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    Quote Originally Posted by spaceship42 View Post
    Give an example of a function f and a set A such that  f \cap A^2 \neq f \upharpoonright A

    Any ideas?
    an idea could be to send f's image outside the set A.

    for example take f:A\rightarrow B, f=\{\left<0,1\right>\}, A=1, B=2.
    Then,  f \cap A^2 = \{\left<0,1\right>\} \cap\{\left<0,0\right>\} = 0,
    but f \upharpoonright A = \{\left<y,x\right>: y\in A \; \& \; \left<y,x\right>\in f\} = \{\left<0,1\right>\}
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