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The 24 pages that link to Intermediate value theorem, each with the reason it gives.

• Continuous functionRelated: Continuity prevents a function from skipping values on an interval.

• ContinuityBroader topic: The theorem supports root-finding by guaranteeing a zero when endpoint values straddle zero.

• Real analysisBroader topic: It proves existence of solutions to equations without requiring an explicit formula.

• Brouwer fixed-point theoremRelated: Brouwer generalizes the one-dimensional fixed-point consequence of this basic continuity theorem.

• Fixed-point theoremCompared with: It guarantees a zero in one dimension, while fixed-point results concern invariant points of maps.

• Extreme value theoremRelated: It is another foundational consequence of continuity on connected domains, though its conclusion differs.

• Bisection methodRelated: Continuity and opposite endpoint signs guarantee a root somewhere in the interval.

• Interval (mathematics)Related: Its conclusion relies on intervals having no gaps.

• Connected spaceRelated: It follows from the connectedness of intervals and characterizes a familiar consequence of connected domains.

• Monotonic functionRelated: Together with strict monotonicity, it gives existence and uniqueness for many equations.

• Mean value theoremRelated: Continuity and connected intervals help explain why derivative values cannot skip the required average.

• Root-finding algorithmRelated: It establishes that a sign-changing interval contains at least one root.

• Completeness of the real numbersRelated: Its proof depends on the real line having no gaps.

• Zero of a functionRelated: Opposite signs at two endpoints guarantee at least one zero between them.

• Descartes' rule of signsRelated: Once root counts are bounded, sign evaluations and continuity can sometimes establish that a root exists.

• Existence theoremBroader topic: It guarantees a root when a continuous function changes sign across an interval.

• Borsuk–Ulam theoremRelated: The one-dimensional Borsuk–Ulam theorem follows by applying it to differences at opposite points.

• Ham sandwich theoremRelated: In one dimension, it supplies the sign-change argument behind the theorem's simplest case.

• Sturm's theoremCompared with: Unlike endpoint sign tests, Sturm's theorem counts all distinct roots without requiring a sign change across each root.

• Cauchy's mean value theoremRelated: Continuity on the closed interval is part of the hypotheses supporting the result.

• Range of a functionRelated: Continuity fills output gaps between attained values on an interval.

• Regula falsiRelated: Opposite endpoint signs guarantee a root inside the interval when the function is continuous.

• Bolzano's theoremNarrower topic: Bolzano's theorem is the zero-value case of this broader result.

• Budan's theoremRelated: It helps turn sign information at interval boundaries into existence claims about roots.