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Thread: Function question

  1. #1
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    Function question

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

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

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