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The 69 pages that link to Rational number, each with the reason it gives.

• Equivalence relationRelated: Rational numbers can be constructed from equivalent pairs of integers.

• Prime factorizationRelated: Prime factors determine whether a fraction reduces and which primes remain in its denominator.

• Cauchy sequenceRelated: A rational sequence can be Cauchy while approaching an irrational number absent from this space.

• Euclidean algorithmRelated: The algorithm reduces a fraction to lowest terms by dividing numerator and denominator by their gcd.

• SupremumRelated: Their missing least upper bounds expose the difference between ordered and complete systems.

• CardinalityRelated: They are dense on the number line yet still countable.

• Positional notationRelated: Finite or repeating positional expansions represent rational numbers.

• Algebraic closureRelated: Their algebraic closure consists of all algebraic numbers, unlike the larger complex closure of the reals.

• DiophantusRelated: Many problems in the Arithmetica seek rational, not exclusively integer, solutions.

• Total orderRelated: The usual numerical order compares every pair of rational numbers.

• Joseph LiouvilleRelated: The theorem measures how closely rational numbers can approach an algebraic irrational.

• PowerRelated: Rational exponents connect powers to roots.

• Quadratic formulaRelated: When the discriminant is a perfect square and coefficients are rational, the roots are rational.

• Cardinal numberRelated: Despite lying densely on the number line, the rationals are countable.

• Computer algebra systemRelated: Exact rational arithmetic avoids rounding errors common when fractions are stored as floating-point numbers.

• Decimal expansionRelated: Rational numbers have decimal expansions that terminate or eventually repeat.

• Long divisionRelated: Dividing integers can produce a fraction whose decimal expansion is finite or repeating.

• OneRelated: One is rational and has many equivalent fractional representations.

• Constructible numberRelated: Integer lengths and their ratios provide the starting quantities for constructible numbers.

• ReciprocalRelated: The reciprocal of a nonzero rational number is rational.

• Archimedean propertyRelated: The rationals satisfy the property despite lacking completeness.

• Equivalence classRelated: A rational number can be constructed as a class of integer-pair representations of the same ratio.

• Inverse Galois problemRelated: The best-known version asks whether every finite group occurs over this field.

• Division by zeroRelated: The standard definition of rational numbers rules out zero denominators at its foundation.

• Nth rootRelated: A rational radicand can have an irrational root, as with the square root of two.

• Cantor–Dedekind axiomRelated: Rational coordinates alone leave gaps that the axiom’s real coordinates fill.

• Kuratowski's closure-complement problemRelated: Their density in the real line makes them a useful starting subset for closure examples.