Linked from

The 17 pages that link to Cantor's theorem, each with the reason it gives.

• Power setRelated: It shows that taking a power set always produces a larger cardinality.

• Continuum hypothesisRelated: It proves the continuum exceeds the natural numbers but does not rule out an intermediate size.

• CardinalityRelated: It proves that no set can have a cardinality as large as its collection of subsets.

• Countable setRelated: It guarantees uncountable sets even when starting with a countable set.

• Surjective functionRelated: It uses the limits of surjective maps to establish that power sets are strictly larger.

• Cantor's diagonal argumentRelated: Its power-set proof uses diagonalization to produce a subset missing from any proposed list.

• Diagonal argumentRelated: The diagonal construction proves that no function from a set onto its power set can be surjective.

• Cardinal numberRelated: It proves that infinite cardinalities have no largest member.

• Infinite setRelated: It shows that no infinite set is as large as its collection of subsets.

• Uncountable setRelated: It guarantees uncountable power sets, including the real numbers' power set relationship.

• Axiom of Power SetRelated: It shows that repeated power-set formation creates ever-larger infinities.

• Cardinality of the continuumRelated: Applied to the natural numbers, it shows the continuum exceeds ℵ₀.