# Triangle inequality

1. Jul 9, 2008

### coverband

Is it possible to write the triangle inequality in 2 ways:

1. d(x,z) <= d(x,y) + d(y,z)
2. d(x,y) <= d(x,z) + d(z,y) ?

If so, are these the only 2 ways?
Thanks

2. Jul 9, 2008

### HallsofIvy

Staff Emeritus
Well, you could say $d(a,b)\le d(a,c)+ d(c,b)$ or $d(x,u)\le d(x,v)+ d(v,u)$ or pretty much any letters you wanted. But I wouldn't say those were "different" any more than I would say the two you give are "different".