OCME · Bilingual mathematics & derivations
Wave6 Second Layer: Orbits, Monotone Limits, Subspace Topology, Chebyshev, Inclusion-Exclusion, Prime Factorization and Digraphs
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- Finite group action
- Equivalence class
- Supremum and infimum
- Sequence limits and exact tail cutoffs
- Usual order on the real numbers
- Topological space
- Subset
- Topological basis
- Markov inequality
- Variance in finite probability models
- Absolute value
- Set operations
- Basic counting principles
- Cardinality comparison of sets
- Mathematical induction
- Prime natural number
- Natural-number divisibility
- Euclidean algorithm
- Greatest common divisor and coprimality
- Binary relations and set projections
- Set
- Orbit of a finite group action
- Monotone bounded sequence convergence theorem
- Subspace topology
- Chebyshev inequality
- Inclusion-exclusion principle
- Unique prime factorization of integers
- Finite directed graph
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.
Finite group action
Existing canonical prerequisite for the new objects in this pulse.
Equivalence class
Existing canonical prerequisite for the new objects in this pulse.
Supremum and infimum
Existing canonical prerequisite for the new objects in this pulse.
Sequence limits and exact tail cutoffs
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.
Topological space
Existing canonical prerequisite for the new objects in this pulse.
Subset
Existing canonical prerequisite for the new objects in this pulse.
Topological basis
Existing canonical prerequisite for the new objects in this pulse.
Markov inequality
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.
Absolute value
Existing canonical prerequisite for the new objects in this pulse.
Set operations
Existing canonical prerequisite for the new objects in this pulse.
Basic counting principles
Existing canonical prerequisite for the new objects in this pulse.
Cardinality comparison of sets
Existing canonical prerequisite for the new objects in this pulse.
Mathematical induction
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 divisibility
Existing canonical prerequisite for the new objects in this pulse.
Euclidean algorithm
Existing canonical prerequisite for the new objects in this pulse.
Greatest common divisor and coprimality
Existing canonical prerequisite for the new objects in this pulse.
Binary relations and set projections
Existing canonical prerequisite for the new objects in this pulse.
Set
Existing canonical prerequisite for the new objects in this pulse.
Orbit of a finite group action
The images of one point under all group elements form its orbit; all orbits partition the point carrier.
Monotone bounded sequence convergence theorem
A nondecreasing real sequence bounded above converges to the supremum of its terms; the nonincreasing bounded-below version converges to the infimum.
Subspace topology
For Y⊆X, the relative topology consists of every intersection of an ambient open set with Y.
Chebyshev inequality
For a variable with finite mean and variance, the probability of absolute deviation at least epsilon is at most variance/epsilon^2.
Inclusion-exclusion principle
The union cardinality of a finite indexed set family is the alternating sum of intersection sizes over every nonempty index subset.
Unique prime factorization of integers
Every positive integer n>1 has a prime factorization whose prime multiset is unique up to factor order.
Finite directed graph
Under the loop-free simple convention, a finite digraph has a finite vertex carrier and an ordered-pair edge set without loops or duplicate same-direction edges.
Path source & status
path-pulse-foundations-20261108 · candidate