## anonymous one year ago please can someone teach me metric space balls in R^2 with examples ?

1. anonymous

D^2

2. anonymous

@zzr0ck3r

3. trwatkins1

D^2

4. zzr0ck3r

balls in R^2 are disks (a circle with the stuff inside). If it is a closed ball we include the outline, if it is not, we don't.

5. anonymous

ok . please give examples

6. zzr0ck3r

|dw:1442530182678:dw| imagine that is filled in.

7. zzr0ck3r

bbiab going to eat. All balls will look like that...

8. trwatkins1

good job @zzr0ck3r

9. anonymous

ok

10. anonymous

i kinow that if i am given a B(15,0.5) THEN THE answer is 15. in a discrete metric but please give such examples in R^2

11. anonymous

welcome back @zzr0ck3r

12. zzr0ck3r

I have given you examples.

13. anonymous

not a picture

14. zzr0ck3r

in R^2 take any point a and radius b then B(a,b) is the disk centered at a with radius b

15. zzr0ck3r

$B((a_0,a_1),b)=\{(x_0,x_1)\in R^2\mid \sqrt{(x_0-a_0)^2+(x_1-a_1)^2} < b\}$

16. anonymous

ok

17. zzr0ck3r

B((1,0),4) |dw:1442534124499:dw|

18. zzr0ck3r

without the border on the circle

19. anonymous

ok thanks. so that should be open ? what about close?

20. zzr0ck3r

change the < to $$\le$$ and include the border on the picture

21. anonymous

ok, thanks very much sir

22. zzr0ck3r

of course