No convergence in Discrete metric - why? If I have a sequence $(x_n)_{n \in \mathbb{N}} := (\cfrac{1}{n},\cfrac{1}{n})$ in $\mathbb{R}^2$
Then why isn't there convergence with respect to the Discrete metric?
for a discrete metric, the distance between $x = \cfrac{1}{n} = y = $ should be $0$ ?

The metric is a function from $\Bbb{R}^2\times \Bbb{R}^2 \to \Bbb{R}^{+}$. So $$d\left((\frac1n,\frac1n),(0,0)\right)=1$$
