d(x,y) = |x-y| / 1+|x-y|
Describe B1(0), open ball of centre 0 and radius 1;
so i've got (|x| / 1+|x|) < 1
Is that enough of a description? Not sure what I could say about Br(a)
And (X,d) a metric space, fix a point o in X
let d1(x,y)= d(x,o) + d(o,y)
if x ≠ y and d1(x,x)=0
Let x ≠ 0, describe Br(x) w.r.t d1 for all possible r
Not sure at all with that one, any hints would be appreciated.
Hello,
Maybe you can try to simplify !
1+|x|>0 for any x. So you can multiply both sides by 1+|x|, without changing the inequality :
which gives , for any x. It means that the inequality is true for any x.
So the open ball is the whole set.
So is or ?And (X,d) a metric space, fix a point o in X
let d1(x,y)= d(x,o) + d(o,y)
if x ≠ y and d1(x,x)=0
Let x ≠ 0, describe Br(x) w.r.t d1 for all possible r
Not sure at all with that one, any hints would be appreciated.
Is d the same as above ?