Triangle Inequality: 2 Ways to Write It?

coverband · Jul 9, 2008

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

HallsofIvy · Jul 9, 2008

Well, you could say [itex]d(a,b)\le d(a,c)+ d(c,b)[/itex] or [itex]d(x,u)\le d(x,v)+ d(v,u)[/itex] 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".

Triangle Inequality: 2 Ways to Write It?

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