different between finite vs undecidable
finite
English
Etymology
From Middle English fynyte, finit, from Latin f?n?tus, perfect passive participle of f?ni? (“I finish; I terminate”), from f?nis (“boundary”).
Pronunciation
- IPA(key): /?fa?na?t/
Adjective
finite (comparative more finite, superlative most finite)
- Having an end or limit; (of a quantity) constrained by bounds; (of a set) whose number of elements is a natural number.
- Synonym: limited
- (grammar, as opposed to infinite or nonfinite) limited by person or number. [from 19th c.]
Antonyms
- infinite, nonfinite, infinitival
- unlimited
- endless
- eternal
- everlasting
Derived terms
Related terms
Translations
Esperanto
Adverb
finite
- past adverbial passive participle of fini
German
Adjective
finite
- inflection of finit:
- strong/mixed nominative/accusative feminine singular
- strong nominative/accusative plural
- weak nominative all-gender singular
- weak accusative feminine/neuter singular
Ido
Pronunciation
- IPA(key): /fi?nite/
Verb
finite
- adverbial past passive participle of finar
Interlingua
Participle
finite
- past participle of finir
Italian
Pronunciation
- IPA(key): /fi?ni.te/
- Hyphenation: fi?nì?te
Adjective
finite
- feminine plural of finito
Verb
finite
- second-person plural present of finire
- second-person plural imperative of finire
- feminine plural past participle of finire
Latin
Pronunciation
- (Classical) IPA(key): /fi??ni?.te/, [fi??ni?t??]
- (Ecclesiastical) IPA(key): /fi?ni.te/, [fi?ni?t??]
Adverb
f?n?te (not comparable)
- To a certain extent, within limits; limited.
- Antonym: ?nf?n?t?
- Definitely, specifically.
Related terms
References
- finite in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
finite From the web:
- what finite mean
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undecidable
English
Etymology
un- +? decidable
Pronunciation
Adjective
undecidable (not comparable)
- (mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
- The first-order procedure SP differs from the proposi-
tional procedure CP°1 in an essential feature. Namely, CP°1
always terminates while SP may run forever as we have seen with
the example immediately after (3.7). This is not a specific
defect of SP. Rather it is known that first-order logic is an
undecidable theory while propositional logic is a decidable
theory. This means that for the latter there are decision pro-
cedures which for any formula decide whether it is valid or
not — and CP°1 in fact is such a decision procedure — while
for the former such decision procedures do not exist in princi-
ple. Thus SP, according to these results for which the reader
is referred to any logic texts such as [End], [DrG] or [Lew],
is of the kind which we may expect, it is a semi-decision
procedure which confirms if a formula is valid but may run
forever for invalid formulas. Therefore, termination by running
out of time or space after any finite number of steps will
leave the question for the validity of a formula unsettled. [...]
- The first-order procedure SP differs from the proposi-
- (mathematics) (of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)
Antonyms
- decidable
Related terms
- noncomputable
Translations
undecidable From the web:
- what are undecidable problems
- what is undecidable language
- what does undecidable mean
- what are undecidable problems in computer science
- what is undecidable problem in daa
- what is undecidable problem in algorithm
- what is undecidable problem in computability
- what does undecidable
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