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The 38 pages that link to Absolute value, each with the reason it gives.

• Real numberRelated: Absolute value expresses distance along the real number line.

• IntegerRelated: It gives an integer's magnitude without regard to its sign.

• Triangle inequalityRelated: On the real line, the triangle inequality becomes |x + y| ≤ |x| + |y|.

• Limit of a functionRelated: The formal definition measures input and output closeness with absolute value.

• Geometric seriesRelated: Infinite geometric convergence depends on whether the common ratio’s absolute value is below one.

• Square rootRelated: For real x, the principal square root of x² is |x|, not always x.

• Absolute convergenceRelated: Taking each term's magnitude removes sign cancellation from the convergence question.

• Cauchy criterionRelated: Absolute differences measure the separation of real sequence terms.

• Conditional convergenceRelated: Taking each term's magnitude removes the cancellation that can enable conditional convergence.

• Euclidean normRelated: In one dimension, the Euclidean norm reduces to the absolute value.

• Limit of a sequenceRelated: Distance from a proposed limit is measured by the absolute value of the difference.

• Lipschitz continuityRelated: For real functions, the defining inequality uses absolute differences in both input and output.

• InequalityRelated: Absolute-value inequalities express bounds on distance from a point.

• Supremum normRelated: Taking absolute values makes the norm measure magnitude regardless of sign.

• Negative numberRelated: It gives a negative number’s magnitude without its sign.

• Bounded functionRelated: Scalar-valued boundedness is expressed by bounding absolute values.

• Root testRelated: The test applies nth roots to term magnitudes, regardless of sign.

• Comparison testRelated: Taking absolute values creates a nonnegative series to which comparison can apply.

• Distance formulaRelated: Coordinate differences may be negative, but their squared contributions are nonnegative.

• ReciprocalRelated: For nonzero x, the reciprocal's absolute value is 1/|x|.

• SubtractionRelated: The absolute difference gives the nonnegative distance between two numbers.

• Sign functionRelated: For nonzero inputs, the sign function equals the input divided by its absolute value.

• Squeeze theoremRelated: Bounding the absolute error by a quantity tending to zero is a common squeeze proof.

• Integrable functionRelated: Integrability tests the total magnitude of a function, not cancellation between positive and negative values.

• Number lineRelated: Distance from the origin gives absolute value a direct geometric meaning.

• Cube rootRelated: The cube root of a negative number is negative, rather than the absolute value’s nonnegative result.

• Nth rootRelated: The principal even root is nonnegative, so √(x²) equals |x| rather than x in general.

• Sign (mathematics)Related: Absolute value records magnitude while discarding sign.

• 0 (number)Related: Zero is the unique integer whose absolute value is zero.