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The 87 pages that link to Real number, each with the reason it gives.

• LogarithmRelated: Real logarithms usually take positive real inputs and produce real exponents.

• Cauchy sequenceRelated: Every Cauchy sequence of real numbers converges to a real number.

• Georg CantorRelated: The real numbers provide Cantor’s central example of an uncountable set.

• SupremumRelated: Every nonempty real set bounded above has a real supremum.

• CardinalityRelated: Cantor's diagonal argument shows their cardinality exceeds that of the natural numbers.

• Cauchy criterionRelated: For real sequences, the criterion is equivalent to convergence in the real numbers.

• Normed vector spaceRelated: Real scalars are a common field over which norms and vector spaces are defined.

• InequalityRelated: Most elementary inequalities compare real numbers or expressions taking real values.

• Polynomial rootRelated: Real roots are the roots visible as horizontal-axis intersections on standard real graphs.

• Complete metric spaceRelated: The usual metric makes the real numbers a central example of a complete space.

• Monotonic functionRelated: Real-valued monotonicity relies on the usual order of real inputs and outputs.

• Total orderRelated: The usual less-than-or-equal relation totally orders the real numbers.

• Cardinal numberRelated: The reals have strictly greater cardinality than the natural numbers.

• InfimumRelated: The real numbers provide familiar examples where bounded sets have infima.

• Integral calculusRelated: Real-valued limits and sums underpin the standard theory of integration.

• Archimedean propertyRelated: The real numbers satisfy the property, providing its standard model.

• Common logarithmRelated: Common logarithms of positive real inputs can take real values, including non-integers.

• Darboux's theoremRelated: The theorem concerns values between real derivative values.

• Local-global principleRelated: The real completion is an archimedean place that must be included in arithmetic tests.

• Real-valued functionRelated: Every output of a real-valued function belongs to this number system.

• ConstructivismRelated: Constructivist and classical accounts differ over which definitions and existence claims about reals are legitimate.

• Pontryagin dualityRelated: It is self-dual, with real frequencies providing its characters.

• Imaginary numberRelated: Imaginary numbers use real numbers as their coefficients.

• Solovay modelRelated: The theorem concerns every set of real numbers belonging to the model.

• Cauchy's convergence testRelated: For real-valued series, completeness ensures Cauchy partial sums converge to a real sum.

• Ostrowski's theoremRelated: The usual absolute value in the classification leads to the real completion.

• Standard part functionRelated: Every standard-part value lies in the real numbers.