Alphabeta MathFluid observable uncertainty and numerical bias budgets — Examples
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1 · Prerequisites
- Binary Operations, Monoids, Groups and Subgroups
- Construction of the Natural Numbers
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Cosets, Index and Lagrange's Theorem
- Countability and Uncountability
- Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
- Finite Counting, Factorials and Binomial Coefficients
- Foundations of the Real Numbers for Analysis
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- IID Monte Carlo integration and error
- Independence Borel Cantelli and Zero One Laws
- limsup, liminf, and Subsequential Limits
- Measurable Functions and Simple Approximation
- Measures and Their Basic Properties
- Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness
- Normal Subgroups and Quotient Groups
- Order, Zorn's Lemma, and the Axiom of Choice
- Pointwise Extended-Real Function Products
- Polynomial Rings, the Division Algorithm and Roots
- Probability Spaces Random Variables and Expectation
- Relations, Functions, and Quotients
- Rings, Subrings, Integral Domains and Fields
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Sigma Algebras and Borel Sets
- Simple Field Extensions and the Construction of the Complex Numbers
- Suprema and Infima
- The Lebesgue Integral and the Convergence Theorems
- The ZFC Axioms and the Basic Set Constructions
- Topological Spaces and Continuity
- Topology of ℝ
- Weak Laws and Series of Independent Random Variables
2 · Logical flowchart
3 · Items
Example