Foundations

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

Classical logic combines truth-valued propositions using defined connectives.

A mathematical proof derives a conclusion within stated assumptions and rules.

A set specifies membership without counting duplicate listings.

A function assigns exactly one output to each input in its domain.

A base case and general successor step establish a predicate on all nonnegative integers.

In a Euclidean right triangle, squared leg lengths sum to the squared hypotenuse length.

Sine and cosine are unit-circle coordinates whose squared values sum to one.

A complex number has real coordinates a and b and an imaginary unit satisfying i²=−1.

A linear map preserves linear combinations and has a matrix once bases are chosen.

A finite limit controls output error through sufficiently small input distance.

A derivative is a finite limit of local difference quotients.

A definite integral is the limiting signed accumulation of small contributions.

Continuity connects differentiation with integration.

A probability assigns nonnegative, normalised, countably additive weights to events.

Conditioning restricts attention to an event of positive probability.

Expected value weights possible values by their probabilities.

A confidence level describes repeated-sampling coverage of an interval procedure.

A bit has two possible states; a fixed-width unsigned binary word encodes an integer.

Shannon entropy measures uncertainty in a specified probability distribution.

An algorithm specifies effective steps; a decision procedure must terminate on every permitted input.

No total algorithm decides halting for every program and input in a general computation model.

Big O bounds eventual growth up to a fixed constant factor.

Seven named base units organize the SI quantity system.

Prefix symbols specify decimal scale factors.

Connect a result to a reference through documented calibrations.

Combine input uncertainty through a measurement model.

Use dimensions to detect impossible quantity equations.

An inverse-square force models attraction between point masses.

Relate a periodic wave's spatial and temporal repetition.