OCME · Bilingual mathematics & derivations
Wave6 Twelfth Layer: CLT, SLLN, Confidence Coverage, Wilson, p-adic Valuations and Regular Languages
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- Independent identically distributed sequence
- Convergence in distribution
- Expectation in finite models
- Variance in finite probability models
- Standard normal distribution
- Sigma-algebras and measure spaces
- Binomial theorem
- Almost-sure convergence
- Sampling distribution
- Statistical estimator
- Parametric statistical model
- Probability on finite sample spaces
- Usual order on the real numbers
- Prime natural number
- Natural-number congruence modulo a positive modulus
- Factorial
- Modular inverse
- Natural-number divisibility
- Unique prime factorization of integers
- Integer
- Absolute value
- Regular language
- Set
- Sequence
- Mathematical induction
- Deterministic finite automaton
- Mathematical proof
- Pigeonhole principle
- Quantifiers and explicit domains
- Central limit theorem for finite-variance IID sequences
- Strong law of large numbers for finite-valued IID sequences
- Confidence-interval coverage in a finite model
- Wilson theorem
- p-adic valuation of integers
- Regular expression
- Pumping lemma for regular languages
Complete seven traceable knowledge objects in dependency order on the existing number-system and function foundations.
This is a suggested learning sequence, not a universal logical dependency or a formal proof.
Independent identically distributed sequence
Existing canonical prerequisite for the new objects in this pulse.
Convergence in distribution
Existing canonical prerequisite for the new objects in this pulse.
Expectation in finite models
Existing canonical prerequisite for the new objects in this pulse.
Variance in finite probability models
Existing canonical prerequisite for the new objects in this pulse.
Standard normal distribution
Existing canonical prerequisite for the new objects in this pulse.
Sigma-algebras and measure spaces
Existing canonical prerequisite for the new objects in this pulse.
Binomial theorem
Existing canonical prerequisite for the new objects in this pulse.
Almost-sure convergence
Existing canonical prerequisite for the new objects in this pulse.
Sampling distribution
Existing canonical prerequisite for the new objects in this pulse.
Statistical estimator
Existing canonical prerequisite for the new objects in this pulse.
Parametric statistical model
Existing canonical prerequisite for the new objects in this pulse.
Probability on finite sample spaces
Existing canonical prerequisite for the new objects in this pulse.
Usual order on the real numbers
Existing canonical prerequisite for the new objects in this pulse.
Prime natural number
Existing canonical prerequisite for the new objects in this pulse.
Natural-number congruence modulo a positive modulus
Existing canonical prerequisite for the new objects in this pulse.
Factorial
Existing canonical prerequisite for the new objects in this pulse.
Modular inverse
Existing canonical prerequisite for the new objects in this pulse.
Natural-number divisibility
Existing canonical prerequisite for the new objects in this pulse.
Unique prime factorization of integers
Existing canonical prerequisite for the new objects in this pulse.
Integer
Existing canonical prerequisite for the new objects in this pulse.
Absolute value
Existing canonical prerequisite for the new objects in this pulse.
Regular language
Existing canonical prerequisite for the new objects in this pulse.
Set
Existing canonical prerequisite for the new objects in this pulse.
Sequence
Existing canonical prerequisite for the new objects in this pulse.
Mathematical induction
Existing canonical prerequisite for the new objects in this pulse.
Deterministic finite automaton
Existing canonical prerequisite for the new objects in this pulse.
Mathematical proof
Existing canonical prerequisite for the new objects in this pulse.
Pigeonhole principle
Existing canonical prerequisite for the new objects in this pulse.
Quantifiers and explicit domains
Existing canonical prerequisite for the new objects in this pulse.
Central limit theorem for finite-variance IID sequences
An infinite IID sequence with common finite positive variance has centered sums scaled by sigma*sqrt(n) converging in distribution to the standard normal law.
Strong law of large numbers for finite-valued IID sequences
The sample means of a finite-valued infinite IID sequence converge almost surely to the common expectation.
Confidence-interval coverage in a finite model
Frequentist coverage is the repeated-sampling probability that a fixed interval-valued procedure covers each true parameter.
Wilson theorem
An integer n>1 is prime exactly when (n−1)! is congruent to−1 modulo n.
p-adic valuation of integers
For prime p and nonzero integer a, v_p(a) is the largest exponent of p dividing |a|; this node fixes v_p(0)=infinity.
Regular expression
Regular expressions recursively build languages from the empty language, epsilon, alphabet symbols, union, concatenation and Kleene star.
Pumping lemma for regular languages
Every regular language has a positive pumping length such that each sufficiently long member word has a split that remains in the language for every pump count.
Path source & status
path-pulse-foundations-20261118 · candidate