$d(x, y) = 1$ for $x \neq y$, and $d(x, x) = 0$

Example · Undergraduate

Definition: discrete metric

Terms

Term	This example	Why
metric	✓	The discrete metric is a metric.
discrete metric	✓
norm	✗	The discrete metric does not come from a norm, because it does not scale: $d(2x, 0) = 1 = d(x, 0)$ for every $x \neq 0$.

Distinctions using this example

• Norm vs. metric vs. inner product

All examples · All distinctions · All definitions