# P-adic metric Strong triangle inequality

1. Feb 11, 2010

### beetle2

Hi Guy's
I was wondering If anyone new of a good link about the P-adic metric Strong triangle inequality. I am trying to constuct a proof to show that the p-adic is a metric space.
Must the proof use the Strong triangle inequality ie

$$d(a,c)\leq$$max$${d(a,b),d(b,c)}$$

or can it use the normal inequality ?

$$d(a,c)\leq d(a,b),d(b,c)$$
$$d(a,c)=\mida-c\mid=\mid(a-b)-(c-b)\mid$$

regards

Last edited: Feb 11, 2010
2. Feb 17, 2010

### g_edgar

Of course the strong triangle inequality implies the (usual) triangle inequality. So if you prove either one of them, you are done.