Math 2.0

Computer science Definition

Alphabet

Builds on Finite set

Definition

An alphabet is a nonempty finite set Σ\Sigma. Its elements are called symbols or letters.

Remarks

Example: Σ={0,1}\Sigma = \set{0, 1} is an alphabet, since it is finite and nonempty. Non-example: the set ℕ\N of natural numbers is not an alphabet in this sense, since it is infinite. Some authors allow infinite alphabets in combinatorics on words, and some allow the empty alphabet; most of automata theory uses the finite nonempty case. The letter Σ\Sigma is the usual name for an alphabet, and Σ∗\Sigma^* is the set of strings over it.

Reading path

To understand this page from the ground up, read these 20 pages in order. The foundations come first.

Show the path as a graph
Element, definition, no evidence levelElementdefinitionProposition, concept, no evidence levelPropositionconceptSet, definition, no evidence levelSetdefinitionImplication, definition, no evidence levelImplicationdefinitionPredicate, definition, no evidence levelPredicatedefinitionOrdered pair, definition, no evidence levelOrdered pairdefinitionExistential quantifier, definition, no evidence levelExistential quantifierdefinitionUniversal quantifier, definition, no evidence levelUniversal quantifierdefinitionCartesian product, definition, no evidence levelCartesian productdefinitionSubset, definition, no evidence levelSubsetdefinitionUniqueness quantifier, definition, no evidence levelUniqueness quantifierdefinitionBinary relation, definition, no evidence levelBinary relationdefinitionFunction, definition, no evidence levelFunctiondefinitionCodomain, definition, no evidence levelCodomaindefinitionInjective function, definition, no evidence levelInjective functiondefinitionSurjective function, definition, no evidence levelSurjective functiondefinitionBijective function, definition, no evidence levelBijective functiondefinitionEquinumerous sets, definition, no evidence levelEquinumerous setsdefinitionFinite set, definition, no evidence levelFinite setdefinitionAlphabet, definition, no evidence levelAlphabetdefinition
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. Proposition concept
  3. Set definition
  4. Implication definition
  5. Predicate definition
  6. Ordered pair definition
  7. Existential quantifier definition
  8. Universal quantifier definition
  9. Cartesian product definition
  10. Subset definition
  11. Uniqueness quantifier definition
  12. Binary relation definition
  13. Function definition
  14. Codomain definition
  15. Injective function definition
  16. Surjective function definition
  17. Bijective function definition
  18. Equinumerous sets definition
  19. Finite set definition
  20. Alphabet definition

Where this leads

10 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Alphabet_(formal_languages)
About this page
TagSEVFW9PNMC
URIm2://SEVFW9PNMC
Kinddefinition
WritingW0 stub
MSC68Q45, 68R15
DefinesAlphabet
UsesFinite set
Changed3 November 2026

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