OCME · Bilingual mathematics & derivations
Wave5 Roots: Subspaces, Topological Covers, Almost-Sure Convergence, Matching, Totient and Finite Automata
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- Real vector space
- Subset
- Quantifiers and explicit domains
- Open and closed sets
- Topological space
- Set operations
- Real random variables on finite sample spaces
- Sequence
- Probability on finite sample spaces
- Sigma-algebras and measure spaces
- Convergence in probability
- Finite simple undirected graphs
- Prime natural number
- Greatest common divisor and coprimality
- Basic counting principles
- Function mapping
- Abstract computational model
- Discrete-time dynamical system
- Set
- Real vector subspace
- Topological closure and interior
- Open cover and subcover
- Almost-sure convergence
- Graph matching
- Euler totient function
- Deterministic finite automaton
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.
Real vector space
Existing canonical prerequisite for the new objects in this pulse.
Subset
Existing canonical prerequisite for the new objects in this pulse.
Quantifiers and explicit domains
Existing canonical prerequisite for the new objects in this pulse.
Open and closed sets
Existing canonical prerequisite for the new objects in this pulse.
Topological space
Existing canonical prerequisite for the new objects in this pulse.
Set operations
Existing canonical prerequisite for the new objects in this pulse.
Real random variables on finite sample spaces
Existing canonical prerequisite for the new objects in this pulse.
Sequence
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.
Sigma-algebras and measure spaces
Existing canonical prerequisite for the new objects in this pulse.
Convergence in probability
Existing canonical prerequisite for the new objects in this pulse.
Finite simple undirected graphs
Existing canonical prerequisite for the new objects in this pulse.
Prime natural number
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.
Basic counting principles
Existing canonical prerequisite for the new objects in this pulse.
Function mapping
Existing canonical prerequisite for the new objects in this pulse.
Abstract computational model
Existing canonical prerequisite for the new objects in this pulse.
Discrete-time dynamical system
Existing canonical prerequisite for the new objects in this pulse.
Set
Existing canonical prerequisite for the new objects in this pulse.
Real vector subspace
A nonempty subset of a real vector space is a subspace when it contains zero and is closed under vector addition and multiplication by every real scalar.
Topological closure and interior
The closure of a set is the intersection of all closed supersets, and its interior is the union of all open subsets, relative to the specified topology.
Open cover and subcover
An open cover consists of open sets in the specified topology whose union contains the target; a subcover selects from that original cover and still covers the same target.
Almost-sure convergence
Random variables on the same probability space converge almost surely when they converge pointwise outside an exceptional set of probability zero.
Graph matching
A matching in a finite graph is an edge subset whose edges share no endpoints; the empty matching is allowed.
Euler totient function
Euler phi(n) counts the representatives coprime to n in a complete residue-representative system, retaining the convention phi(1)=1.
Deterministic finite automaton
A DFA consists of finite states, a finite alphabet, a total transition function, one initial state and a subset of accepting states.
Path source & status
path-pulse-foundations-20261101 · candidate