Proving that a metric is non-negative
Solution 1:
$$0 = d(x,x) \leq d(x,y) + d(y,x) = 2 d(x,y) $$
and so
$$ d(x,y) \geq 0 $$
Proving that a metric is non-negative
Solution 1:
$$0 = d(x,x) \leq d(x,y) + d(y,x) = 2 d(x,y) $$
and so
$$ d(x,y) \geq 0 $$
$$0 = d(x,x) \leq d(x,y) + d(y,x) = 2 d(x,y) $$
and so
$$ d(x,y) \geq 0 $$