Alphabeta MathQuantitative Induced Density and the Log-Log Step: Examples
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1 · Prerequisites
- Absolute and Conditional Convergence; Rearrangement; Products
- Binary Operations, Monoids, Groups and Subgroups
- Blockades, Combs and Pattern Graphs
- Compactness in Metric Spaces
- Completeness, Completion, and Uniform Continuity
- Construction of the Natural Numbers
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Continuity, IVT, EVT, and Uniform Continuity
- Countability and Uncountability
- Finite Counting, Factorials and Binomial Coefficients
- Foundations of the Real Numbers for Analysis
- Graphs, Walks and Connectivity
- Inclusion–Exclusion, the Pigeonhole Principle and Double Counting
- Induced Subgraphs and Hereditary Graph Classes
- Limits of Real Functions
- limsup, liminf, and Subsequential Limits
- Metric Spaces
- Monotone Functions, Discontinuities, and Continuity Sets
- Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness
- Order, Zorn's Lemma, and the Axiom of Choice
- Power Series and Real-Analytic Functions
- Properties of the Integral and the Working FTC
- Quantitative Induced Density and the Log-Log Step
- Regular Pairs and Induced Counting
- Relations, Functions, and Quotients
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Sequences and Series of Functions; Uniform Convergence
- Series: Convergence and the Nonnegative Tests
- Sparse Restricted Subgraphs and the Rödl–Nikiforov Theorems
- Suprema and Infima
- The Derivative and the Mean Value Theorems
- The Exponential Function
- The Logarithm and General Powers
- The Riemann Integral: Definition and Integrability
- The ZFC Axioms and the Basic Set Constructions
- Topology of ℝ
- Vector Spaces, Linear Subspaces, Span and Direct Sums
2 · Logical flowchart
3 · Items
Example
A labelled blowup and its good copies
Example
Checking the subreciprocal condition for the quadratic log bound
Example
Checking the subreciprocal condition for the loglog bound
Example