## walters 3 years ago show that if X and Y are Metric spaces with distances dx and dy then

1. anonymous

$D\left(\begin{matrix}x _{1}\\ y _{1}\end{matrix}\right);\left(\begin{matrix}x _{2} \\ y _{2}\end{matrix}\right)$=max( $d _{x}(x _{1};x _{2});d _{y}(y _{1},y _{2})$)

2. anonymous

@saifoo.khan

3. anonymous

is there a part missing from this question?

4. anonymous

yes |dw:1361560088275:dw| the brackets

5. anonymous

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?

6. anonymous

my guess is that you are asked to show that D IS a metric on the product space, where $D((x_1,y_1),(x_2,y_2):=\max d_x(x_1,x_2), d_y(y_1,y_2)$

7. anonymous

|dw:1361560337199:dw|

8. anonymous

are you trying to prove that it is a metric?

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

i 've shown them but it is just that i am not show about the meaning of the question

14. anonymous

me neither, but that seems to me all it CAN mean