Notation and terminology
Shared conventions for logic, algebra, calculus, linear algebra, probability, and statistics.
Global conventions
- \(\mathbb{N}=\{0,1,2,\ldots\}\) unless a lesson explicitly states otherwise.
- Intervals use brackets for included finite endpoints and parentheses for excluded endpoints and for \(\pm\infty\).
- \(=\) asserts equality; \(\approx\) marks approximation; \(\equiv\) marks an identity or congruence as defined by context.
- Vectors are bold lowercase, matrices bold uppercase, and scalars italic.
- Random variables are uppercase and their observed values lowercase.
- Decimal points use a period. Group large numbers with thin spaces in prose.
Precision language
A value is exact when no rounding or numerical approximation was used. A value is approximate when rounded or numerically computed, simulated when produced by a random mechanism, and estimated when inferred from data.
Every symbol must be defined near first use, and every equation must be read in its domain. Notation is a compression device, not a substitute for meaning.