# Is it true that any metric on a finite set is the discrete metric?

• Is it true that any metric on a finite set is the discrete metric?

I can see that it's at least equivalent with the discrete metric since $B(x,\delta)=\{x\}$ where $X=\{a_i\}_{i=1}^n,$ $\delta=\min\{d(a_i,a_j):i\ne j\}, d$ being the metric on $X.$

-