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

• Real numberCompared with: Unlike the reals, the rationals alone are not complete and leave gaps.

• IntegerNarrower topic: Every integer is rational because it can be written with denominator one.

• DivisibilityCompared with: Unlike integer divisibility, rational ratios between nonzero integers always exist.

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

• Finite fieldCompared with: The rational numbers form an infinite field, unlike every finite field.

• Natural numberCompared with: Rationals include fractions that are not natural numbers.

• Diophantine equationNarrower topic: Some Diophantine problems ask for rational points rather than integer solutions.

• 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.

• Algebraic numberBroader topic: Every rational number is algebraic, satisfying a linear integer-coefficient equation.

• Field (mathematics)Broader topic: The rational numbers provide a familiar infinite example of a field.

• Irrational numberCompared with: Irrational numbers are precisely the real numbers excluded from this class.

• Continued fractionNarrower topic: Finite simple continued fractions represent exactly the rational numbers.

• 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.

• Countable setBroader topic: Fractions can be arranged in a sequence despite having infinitely many values.

• Interval (mathematics)Compared with: A rational interval can omit irrational points, so it is not an interval in the real line.

• Transcendental numberNarrower topic: Rational numbers are automatically algebraic, so transcendence implies irrationality.

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

• Cantor setCompared with: Rational points are countable and dense, unlike the uncountable Cantor set, which contains no interval.

• Complete metric spaceCompared with: With the usual distance, rational numbers are not complete: rational Cauchy sequences can converge to irrationals.

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

• Connected spaceCompared with: The rationals inherit a topology from the real line but are disconnected by irrational cut points.

• Diophantine approximationNarrower topic: Rational numbers are the approximants whose closeness to a target is measured.

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

• FieldBroader topic: The rational numbers form the smallest field containing the integers.

• Cantor's diagonal argumentCompared with: Unlike all real numbers, the rational numbers can be enumerated.

• Lindemann–Weierstrass theoremBroader topic: Rational numbers form the coefficient field used in defining algebraic numbers.

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

• Boundary (topology)Broader topic: The rationals have the entire real line as their boundary in the usual topology.

• 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.

• Dedekind cutNarrower topic: The cut divides this ordered number system into its lower and upper sets.

• Division ringBroader topic: The rationals are a basic commutative example satisfying the division-ring axioms.

• 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.

• Algebraic integerCompared with: A rational number is an algebraic integer exactly when it is an ordinary integer.

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

• Dirichlet's approximation theoremCompared with: Rational targets have exact representations, unlike the nontrivial approximations needed for irrationals.

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

• Fixed-point arithmeticCompared with: Rational representations can preserve some fractions exactly where fixed-point quantizes them.

• p-adic valuationNarrower topic: The valuation extends the integer exponent by taking numerator minus denominator exponents.

• Completeness of the real numbersCompared with: The rationals form an ordered field but fail the least-upper-bound property.