Maths for ML / Notation

\lim_{x\to a} f(x)

limit

CalculusIntermediate

Say it “the limit as x approaches a of f of x”

The value f gets closer and closer to as x approaches a.

Example

\lim_{x\to\infty} \sigma(x) = 1

The sigmoid saturates at 1.

Where you’ll see it in ML

Saturation of activations; the definition of the derivative.

Don’t confuse it with

$\infty$ infinity Bigger than any number — used in limits and ranges, not as an actual value.
$f: \mathbb{R}^{n} \to \mathbb{R}$ function arrow (type) Says what kind of input a function takes and what kind of output it gives — its type signature.

Lessons that use it

The derivative: slope, and sensitivity

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