Matthollyw00d
Sep30-09, 11:06 AM
D={z in C | |z|<1}
e: DxD -> R by e(z,w)=|(z-w)/(1-w'z)| (here the w'=the conjugate of w, not sure how to insert a bar on top of the w). Show that this is a metric space. It's all pretty easy till the triangle inequality (as always though, right?) so that's all I need to focus on. I'm pretty lost on where to start for this one. I've tried several manipulations and even tried working with this all in a+bi form, and never really saw any good place to insert a +/-x and make an inequality. Any help?
e: DxD -> R by e(z,w)=|(z-w)/(1-w'z)| (here the w'=the conjugate of w, not sure how to insert a bar on top of the w). Show that this is a metric space. It's all pretty easy till the triangle inequality (as always though, right?) so that's all I need to focus on. I'm pretty lost on where to start for this one. I've tried several manipulations and even tried working with this all in a+bi form, and never really saw any good place to insert a +/-x and make an inequality. Any help?