Maths for ML / Notation

\{x \mid P(x)\}

set-builder notation

SetsBeginner

Say it “the set of x such that…”

Describes a set by a rule: everything before the bar, filtered by the condition after it.

Example

\{x \in \mathbb{R} \mid x > 0\}

All positive real numbers.

In code

[x for x in xs if x > 0]

Where you’ll see it in ML

Defining feasible regions and decision regions.

Don’t confuse it with

$a \mid b$ vertical bar — many meanings Context decides: 'given' in probability, 'such that' in set-builder, 'divides' in number theory. Two bars ‖ mean a norm or KL divergence.
$P(A \mid B)$ conditional probability Probability of A, once you know B happened. The bar means 'given'.

Lessons that use it

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