OCME · Bilingual mathematics & derivations
First Extended Atlas Slice: Topology, Number Theory, Decision Problems, and Formal Statements
On this page
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.
Set
Existing canonical prerequisite for the new objects in this pulse.
Set operations
Existing canonical prerequisite for the new objects in this pulse.
Natural number
Existing canonical prerequisite for the new objects in this pulse.
Arithmetic operations
Existing canonical prerequisite for the new objects in this pulse.
Proposition
Existing canonical prerequisite for the new objects in this pulse.
Function mapping
Existing canonical prerequisite for the new objects in this pulse.
Topological space
A topological space consists of an underlying set and a family of open sets containing the empty set and whole space and closed under arbitrary unions and finite intersections.
Natural-number divisibility
A natural number a divides b when a natural multiplier k satisfies b=a·k; the two roles of zero must be distinguished.
Greatest common divisor and coprimality
The natural number gcd(a,b) divides both a and b and is divisible by every common divisor; the inputs are coprime when their gcd is 1.
Prime natural number
A prime natural number is at least 2 and has no positive divisors other than 1 and itself.
Natural-number congruence modulo a positive modulus
For a fixed positive modulus n, two natural numbers a and b are congruent modulo n when they have the same remainder on division by n.
Decision problem
A decision problem specifies an input set X and a yes-instance subset Y⊆X; a decider must terminate on every legal input and return the correct Boolean answer.
Formal statements in a proof assistant
A formal statement is a core term of type Prop obtained by successful elaboration in a fixed version, import environment and local context.
Path source & status
path-pulse-foundations-20261018 · candidate