anonymous
  • anonymous
please can someone teach me metric space balls in R^2 with examples ?
Mathematics
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katieb
  • katieb
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anonymous
  • anonymous
D^2
anonymous
  • anonymous
@zzr0ck3r
trwatkins1
  • trwatkins1
D^2

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zzr0ck3r
  • 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.
anonymous
  • anonymous
ok . please give examples
zzr0ck3r
  • zzr0ck3r
|dw:1442530182678:dw| imagine that is filled in.
zzr0ck3r
  • zzr0ck3r
bbiab going to eat. All balls will look like that...
trwatkins1
  • trwatkins1
good job @zzr0ck3r
anonymous
  • anonymous
ok
anonymous
  • 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
anonymous
  • anonymous
welcome back @zzr0ck3r
zzr0ck3r
  • zzr0ck3r
I have given you examples.
anonymous
  • anonymous
not a picture
zzr0ck3r
  • zzr0ck3r
in R^2 take any point a and radius b then B(a,b) is the disk centered at a with radius b
zzr0ck3r
  • zzr0ck3r
\[B((a_0,a_1),b)=\{(x_0,x_1)\in R^2\mid \sqrt{(x_0-a_0)^2+(x_1-a_1)^2} < b\}\]
anonymous
  • anonymous
ok
zzr0ck3r
  • zzr0ck3r
B((1,0),4) |dw:1442534124499:dw|
zzr0ck3r
  • zzr0ck3r
without the border on the circle
anonymous
  • anonymous
ok thanks. so that should be open ? what about close?
zzr0ck3r
  • zzr0ck3r
change the < to \(\le\) and include the border on the picture
anonymous
  • anonymous
ok, thanks very much sir
zzr0ck3r
  • zzr0ck3r
of course

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