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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.

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

• 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.

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

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

• 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.

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

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

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

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

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

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

• Even numberCompared with: Divisibility by 2 defines evenness for integers, not for rational numbers.

• Square root of 2Compared with: No fraction of integers equals square root of 2, although fractions can approximate it.

• Apéry's theoremCompared with: The proof assumes ζ(3) has this form, then derives a contradiction.

• Proof that π is irrationalCompared with: Rational numbers have eventually repeating decimal expansions, unlike π.