# Wave-One Domain Foundations

Branch from natural numbers, sets, and propositions into arithmetic, equations, probability, induction, factorials, and elementary combinatorial counting.

[← Return to results](/en/paths/)

This is a suggested learning sequence, not a universal logical dependency or a formal proof.


- Stage 1 · required



## [Natural number](/en/mko/mko-natural-number/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Supply the natural-number foundation for arithmetic, induction, and finite counting.

[Related questions](/en/explore/?mko=mko-natural-number) [Concept guides](/en/derivations/?q=mko-natural-number)


- Stage 1 · required



## [Set](/en/mko/mko-set/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Supply the set foundation for treating a sample space as a collection of outcomes.

[Related questions](/en/explore/?mko=mko-set) [Concept guides](/en/derivations/?q=mko-set)


- Stage 1 · required



## [Proposition](/en/mko/mko-proposition/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Supply the logical foundation for proposition families handled by induction.

[Related questions](/en/explore/?mko=mko-proposition) [Concept guides](/en/derivations/?q=mko-proposition)


- Stage 2 · required



## [Arithmetic operations](/en/mko/mko-arithmetic-operations/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Unlock quantitative combination in algebraic expressions and elementary counting.

[Related questions](/en/explore/?mko=mko-arithmetic-operations) [Concept guides](/en/derivations/?q=mko-arithmetic-operations)


- Stage 2 · optional



## [Sample space](/en/mko/mko-sample-space/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Move from set language into the outcome domain of probability and statistics.

[Related questions](/en/explore/?mko=mko-sample-space) [Concept guides](/en/derivations/?q=mko-sample-space)


- Stage 2 · optional



## [Mathematical induction](/en/mko/mko-mathematical-induction/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Move from natural numbers and propositions into a structured proof method.

[Related questions](/en/explore/?mko=mko-mathematical-induction) [Concept guides](/en/derivations/?q=mko-mathematical-induction)


- Stage 3 · optional



## [Variables and algebraic expressions](/en/mko/mko-variable-expression/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Move from arithmetic operations into algebraic expressions containing variables.

[Related questions](/en/explore/?mko=mko-variable-expression) [Concept guides](/en/derivations/?q=mko-variable-expression)


- Stage 3 · optional



## [Basic counting principles](/en/mko/mko-counting-principle/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Combine counts of finite choices using natural numbers and arithmetic operations.

[Related questions](/en/explore/?mko=mko-counting-principle) [Concept guides](/en/derivations/?q=mko-counting-principle)


- Stage 3 · optional



## [Factorial](/en/mko/mko-factorial/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Use natural-number multiplication and successor recursion to build a finite product.

[Related questions](/en/explore/?mko=mko-factorial) [Concept guides](/en/derivations/?q=mko-factorial)


- Stage 4 · optional



## [Equation](/en/mko/mko-equation/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Move from expressions into equality, solution sets, and substitution checks.

[Related questions](/en/explore/?mko=mko-equation) [Concept guides](/en/derivations/?q=mko-equation)


- Stage 5 · optional



## [Linear equation in one variable](/en/mko/mko-linear-equation/?from=%2Fen%2Fpaths%2Fpath-domain-coverage-wave-one%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Use a nonzero linear coefficient to obtain a unique solution and distinguish the degenerate constant cases.

[Related questions](/en/explore/?mko=mko-linear-equation) [Concept guides](/en/derivations/?q=mko-linear-equation)



Path source & statuspath-domain-coverage-wave-one · candidate

[Original paths JSON](/data/architecture/learning-paths.json)