I don't care, everyone's same to me

 The discrete metric is the Mathematician's version of "I don't care, everyone's same to me." Formally, for a set X, The discrete metric $d:X\times X \to \mathbb{R}^{+}$ is defined as

$$ d(x,y) = \begin{cases} 0 & \text{if } x = y \\ 1 & \text{if } x \neq y \end{cases} $$

So if $x$ and $y$ are the same, the distance is 0 - because clearly, no one can run away from themselves. If $x$ and $y$ are different, the distance is 1, whether they're a millimeter apart or living in alternate dimensions.

Basically, it's the "I'm too  busy to calculate actual distances" metric, treating every set like a collection of socially distant points at a fixed, no-questions-asked distance from one.