Question

please help,

Answer 1

let x be an arbitary non-empty set and p: X*X---> R be discrete metric on x, defined by p(x,y)= k^2 - 4 if x \[\neq y\] and 0 if x=y ... obtain the possible values of k

Answer 2

@zzr0ck3r , @Kainui , @oldrin.bataku

Answer 3

@dan815

Answer 4

@Loser66

Answer 5

@zzr0ck3r , @Kainui , @oldrin.bataku

Answer 6

@Loser6

Answer 7

@dan815

Answer 8

what is the first rule of being a metric?

Answer 9

I think if \(x\neq y\) then the distance between them \(\neq 0\) and = k^2 -4
Moreover, the distance is never negative, hence k^2 -4 >0 and k<-2 or k >2

Answer 10

The discrete metric just puts the same distance between all points (think integers).

1st rule of metric club is that we only obtain non negative values. i.e. \[K^2-4\ge 0\]

Answer 11

@zzr0ck3r cannot be =0, right?

Answer 12

but at that time, x =y while we are considering \(x\neq y\)

Answer 13

Because it is a piece wise function.