# Math Help - Function question

1. ## 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?

2. Originally Posted by spaceship42
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 $f \upharpoonright A = \{\left: y\in A \; \& \; \left\in f\} = \{\left<0,1\right>\}$