d(x,y)=(x−y)2
isn't a metric on R. Its triangular inequality doesn't holds.
As I did
d(x,z)=((x−y)+(y−z))2=(x−y)2+(y−z)2+2(x−y)(y−z)
As, a2+b2<a2+b2+2ab ,so we can say that (x−y)2+(y−z)2<(x−y)2+(y−z)2+2(x−y)(y−z) this implies that d(x,z)>d(x,y)+d(y,z). Am I right ?
