Here's the question you clicked on:
walters
show that if X and Y are Metric spaces with distances dx and dy then
\[D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)\]=max( \[d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})\])
is there a part missing from this question?
yes |dw:1361560088275:dw| the brackets
i still think there is something missing X and Y are metric spaces, with some metric defined on each what does \((x_1,y_1)\) mean? are you trying to define a metric on the product?
my guess is that you are asked to show that D IS a metric on the product space, where \[D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)\]
are you trying to prove that it is a metric?
i don't understand wat the question means does it means i have to prove that LHS=RHS or showing that it is the metric space
that is, you are defining the metric on the product as the max of the distances component wise, and you need to check that is satisfies all the axioms of a metric space
that is what i was asking what is the actual question it looks like you have defined a metric, and you want to prove that it is one, that is, that is satisfies the axioms
so for example you need to check that \[D\left((x_1,y_1), (x_2,y_2)\right)=0\iff (x_1,y_1)=(x_2,y_2)\] etc, that is check each axiom
i 've shown them but it is just that i am not show about the meaning of the question
me neither, but that seems to me all it CAN mean