Math 2.0

Mathematical logic and foundations Set theory: axioms and basics Concept

Class

Builds on SetZermelo–Fraenkel set theoryRussell's paradoxOrdinal number

Summary

In set theory, a class is a collection of sets defined by a property that all its members share. Every set is a class, but some classes are too large to be sets; these are the proper classes. Examples of proper classes are the class of all sets and the class of all ordinals. Classes let one speak about such large collections without the contradictions of Russell's paradox.

Reading path

To understand this page from the ground up, read these 25 pages in order. The foundations come first.

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Element, definition, no evidence levelElementdefinitionOrdinal number, concept, no evidence levelOrdinal numberconceptProposition, concept, no evidence levelPropositionconceptSet, concept, no evidence levelSetconceptSet, definition, no evidence levelSetdefinitionConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptModus ponens, concept, no evidence levelModus ponensconceptUniversal quantifier, definition, no evidence levelUniversal quantifierdefinitionAxiom of extensionality, statement, no evidence levelAxiom of extensionali…statementMathematical proof, concept, no evidence levelMathematical proofconceptPropositional logic, concept, no evidence levelPropositional logicconceptTautology, definition, no evidence levelTautologydefinitionPredicate logic, concept, no evidence levelPredicate logicconceptLogical equivalence, definition, no evidence levelLogical equivalencedefinitionZermelo–Fraenkel set theory, concept, no evidence levelZermelo–Fraenkel set …conceptDouble negation law, statement, no evidence levelDouble negation lawstatementProof by contradiction, concept, no evidence levelProof by contradictionconceptRussell's paradox, statement, no evidence levelRussell's paradoxstatementClass, concept, no evidence levelClassconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Element definition
  2. Ordinal number concept
  3. Proposition concept
  4. Set concept
  5. Set definition
  6. Conjunction definition
  7. Disjunction definition
  8. Implication definition
  9. Negation definition
  10. Predicate definition
  11. Biconditional definition
  12. Truth table concept
  13. Modus ponens concept
  14. Universal quantifier definition
  15. Axiom of extensionality statement
  16. Mathematical proof concept
  17. Propositional logic concept
  18. Tautology definition
  19. Predicate logic concept
  20. Logical equivalence definition
  21. Zermelo–Fraenkel set theory concept
  22. Double negation law statement
  23. Proof by contradiction concept
  24. Russell's paradox statement
  25. Class concept

Where this leads

7 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Class_(set_theory)
About this page
TagY48FA69563
URIm2://Y48FA69563
Kindconcept
WritingW0 stub
MSC03E30, 03E70
UsesSet, Zermelo–Fraenkel set theory, Russell's paradox, Ordinal number
Same as
Changed2 November 2026

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