Foundations

Classical logic combines truth-valued propositions using defined connectives.

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.

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 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.

Microstate probabilities quantify statistical entropy.

A density operator represents quantum statistical states.

A joint pure state can fail to factor into subsystem states.

Sample the joint input model to approximate the output distribution.

An ideal baseband signal containing no frequencies above B can be reconstructed from exact uniform samples at f_s>2B.

For a uniform rounding quantizer with step Δ and no overload, the error magnitude is at most Δ/2.