Metric that isn't translation-invariant?

[Anonymous217]

I'm having trouble thinking of an example of one. I'm aware that all metrics induced by a norm are translation-invariant, but I can't think of any example of a metric that isn't induced by a norm. I guess I'm stuck focusing on one aspect and I can't think of a simple example.

 

[losiu99]

How about reals and $$d=|x^3-y^3|$$?

 

[Anonymous217]

Can't believe I didn't think of that. Thanks so much!