Gödel numbering
Formulas become integers
Gödel numbering is a method of encoding mathematical statements and proofs as unique natural numbers, developed by logician Kurt Gödel.
The technique assigns a distinct integer to each symbol, formula, and sequence of formulas in a formal system, allowing statements about mathematics to be expressed as statements about numbers.
This self-referential capacity was central to Gödel's incompleteness theorems, which showed that sufficiently powerful mathematical systems contain true statements that cannot be proved within the system.
incompleteness
Pointing to oneself
- fixed pointValue unchanged by function
- consistencyReliable adherence to standards
- completenessState of being whole
- undefinabilityState beyond precise description
computability
Formal models of computation
- Church-Turing thesisEffective procedures equal algorithms
- enumerationSequential listing of items
- decidabilityAlgorithmic resolution capability
- algorithmFinite problem-solving procedure
encoding
Unique prime product representation
- binaryConsisting of two parts
- concatenationJoining items end-to-end
- exponentiationRaising to a power
- divisibilityAbility to divide evenly
self-reference
Pointing to oneself
- fixed pointValue unchanged by function
- consistencyReliable adherence to standards
- completenessState of being whole
Turing machines
Formal models of computation
- Church-Turing thesisEffective procedures equal algorithms
- enumerationSequential listing of items
- decidabilityAlgorithmic resolution capability
prime factorization
Unique prime product representation
- binaryConsisting of two parts
- concatenationJoining items end-to-end
- exponentiationRaising to a power
Vienna
Austrian capital