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In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was famously used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931)
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of strings. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.
Since Gödel's paper was published in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
Gödel noted that statements within a system can be represented by natural numbers. The significance of this was that properties of statements - such as their truth and falsehood - would be equivalent to determining whether their Gödel numbers had certain properties. The numbers involved might be very long indeed (in terms of number of digits), but this is not a barrier; all that matters is that we can show such numbers can be constructed.
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Gödel_numbering
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931) A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the pub -
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Fermat's "Little" Theorem is great - but beware of Fermat Liars and tricky Carmichael Numbers. Continues at: http://youtu.be/HvMSRWTE2mI Featuring Dr James Grime - https://twitter.com/jamesgrime Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Google Plus: http://bit.ly/numberGplus Tumblr: http://numberphile.tumblr.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran A run-down of Brady's channels: http://bit.ly/bradychannels -
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Gödel's Incompleteness Theorem Explained Part 1: Formal Systems and Gödel Numbering
- Order: Reorder
- Duration: 13:10
- Updated: 27 Aug 2014
- author: BestThingWorstThing
Temporary notice: This series is not yet complete. If you'd really like to see it continue, it would help me a lot if you liked or subscribed. Thank you! Ver...
http://wn.com/Gödel's_Incompleteness_Theorem_Explained_Part_1_Formal_Systems_and_Gödel_Numbering
Temporary notice: This series is not yet complete. If you'd really like to see it continue, it would help me a lot if you liked or subscribed. Thank you! Ver...
- published: 07 Apr 2014
- views: 1908
- author: BestThingWorstThing
Gödel's Incompleteness Theorem Explained Part 3: Introduction to Typographical Number Theory
- Order: Reorder
- Duration: 23:10
- Updated: 04 Sep 2014
- author: BestThingWorstThing
Thanks to everyone who gave me feedback on part 2! Now it's time to explain how formal systems can be used to do number theory. Feel free to ask me any quest...
http://wn.com/Gödel's_Incompleteness_Theorem_Explained_Part_3_Introduction_to_Typographical_Number_Theory
Thanks to everyone who gave me feedback on part 2! Now it's time to explain how formal systems can be used to do number theory. Feel free to ask me any quest...
- published: 13 Jul 2014
- views: 198
- author: BestThingWorstThing
Gödel's Incompleteness Theorem Explained Part 4: Properties and Relations of Numbers in TNT
- Order: Reorder
- Duration: 18:35
- Updated: 11 Aug 2014
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Part 4 of 5 in my series on Gödel's Incompleteness Theorem. As always, based heavily on Douglas R. Hofstadter's book Gödel, Escher, Bach: An Eternal Golden B...
http://wn.com/Gödel's_Incompleteness_Theorem_Explained_Part_4_Properties_and_Relations_of_Numbers_in_TNT
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- views: 75
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Theory of Computation: Gӧdel Numbers (Part 01)
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http://wn.com/Theory_of_Computation_Gӧdel_Numbers_(Part_01)
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- published: 14 Apr 2012
- views: 481
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B3. Godel Numbering and Incompleteness
- Order: Reorder
- Duration: 50:05
- Updated: 31 May 2014
- author: Per Stinchcombe
http://wn.com/B3._Godel_Numbering_and_Incompleteness
Gödel numbering
- Order: Reorder
- Duration: 7:34
- Updated: 05 Aug 2015
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931) A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
http://wn.com/Gödel_numbering
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931) A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
- published: 05 Aug 2015
- views: 1
Secure Data-Transmission through Images using Godel Numbering
- Order: Reorder
- Duration: 14:34
- Updated: 06 Dec 2012
- author: deepak murthy
Course project for EEL6562.
http://wn.com/Secure_Data-Transmission_through_Images_using_Godel_Numbering
Gödel's Incompleteness Theorems: History, Proofs, Implications
http://thebrooklyninstitute.com/bisr_course/godels-incompleteness-theorems-history-proofs-implications/ In 1931, a 25-year-old Kurt Gödel published a paper i...
http://wn.com/Gödel's_Incompleteness_Theorems_History,_Proofs,_Implications
http://thebrooklyninstitute.com/bisr_course/godels-incompleteness-theorems-history-proofs-implications/ In 1931, a 25-year-old Kurt Gödel published a paper i...
- published: 30 Jan 2013
- views: 3262
- author: ajayc42
TennGitarMan2
- Order: Reorder
- Duration: 5:53
- Updated: 28 Feb 2014
C open position tuning.
http://wn.com/TennGitarMan2
C open position tuning.
- published: 28 Feb 2014
- views: 0
Gödel number Meaning
- Order: Reorder
- Duration: 0:29
- Updated: 11 May 2015
Video shows what Gödel number means. A number uniquely assigned to each symbol, and to each well-formed formula of some formal language.. Gödel number Meaning. How to pronounce, definition audio dictionary. How to say Gödel number. Powered by MaryTTS, Wiktionary
http://wn.com/Gödel_number_Meaning
Video shows what Gödel number means. A number uniquely assigned to each symbol, and to each well-formed formula of some formal language.. Gödel number Meaning. How to pronounce, definition audio dictionary. How to say Gödel number. Powered by MaryTTS, Wiktionary
- published: 11 May 2015
- views: 0
- published: 28 Feb 2014
- views: 0
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
- Order: Reorder
- Duration: 15:00
- Updated: 02 Sep 2014
- author: globalbeehive
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel ...
http://wn.com/Kurt_Godel_The_World's_Most_Incredible_Mind_(Part_1_of_3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel ...
- published: 18 Oct 2011
- views: 107016
- author: globalbeehive
Kurt Godel: The World's Most Incredible Mind (Part 2 of 3)
- Order: Reorder
- Duration: 15:00
- Updated: 01 Sep 2014
- author: globalbeehive
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel ...
http://wn.com/Kurt_Godel_The_World's_Most_Incredible_Mind_(Part_2_of_3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel ...
- published: 05 Nov 2011
- views: 40806
- author: globalbeehive
Kurt Godel: The World's Most Incredible Mind (Part 3 of 3)
- Order: Reorder
- Duration: 14:55
- Updated: 19 Aug 2013
- author: globalbeehive
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel ...
http://wn.com/Kurt_Godel_The_World's_Most_Incredible_Mind_(Part_3_of_3)
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- published: 10 Nov 2011
- views: 16970
- author: globalbeehive
Professor Rebecca Goldstein - Gödel's Incompleteness Theorems in the Context of Philosophy
- Order: Reorder
- Duration: 79:13
- Updated: 30 Aug 2014
- author: NCHumanities
Rebecca Goldstein's first lecture in a series of four addresses Gödel's Incompleteness Theorems. The philosophical implications of mathematics and its beauti...
http://wn.com/Professor_Rebecca_Goldstein_-_Gödel's_Incompleteness_Theorems_in_the_Context_of_Philosophy
Rebecca Goldstein's first lecture in a series of four addresses Gödel's Incompleteness Theorems. The philosophical implications of mathematics and its beauti...
- published: 05 Aug 2013
- views: 6403
- author: NCHumanities
Isomorphic Types on Graphs: One-Neighborhood Godel Sections
- Order: Reorder
- Duration: 0:16
- Updated: 10 Oct 2013
- author: wolframmathematica
http://demonstrations.wolfram.com/IsomorphicTypesOnGraphsOneNeighborhoodGoedelSections The Wolfram Demonstrations Project contains thousands of free interact...
http://wn.com/Isomorphic_Types_on_Graphs_One-Neighborhood_Godel_Sections
http://demonstrations.wolfram.com/IsomorphicTypesOnGraphsOneNeighborhoodGoedelSections The Wolfram Demonstrations Project contains thousands of free interact...
- published: 08 Sep 2010
- views: 711
- author: wolframmathematica
Liar Numbers - Numberphile
- Order: Reorder
- Duration: 7:09
- Updated: 03 Feb 2014
Fermat's "Little" Theorem is great - but beware of Fermat Liars and tricky Carmichael Numbers.
Continues at: http://youtu.be/HvMSRWTE2mI
Featuring Dr James Grime - https://twitter.com/jamesgrime
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Google Plus: http://bit.ly/numberGplus
Tumblr: http://numberphile.tumblr.com
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
A run-down of Brady's channels: http://bit.ly/bradychannels
http://wn.com/Liar_Numbers_-_Numberphile
Fermat's "Little" Theorem is great - but beware of Fermat Liars and tricky Carmichael Numbers.
Continues at: http://youtu.be/HvMSRWTE2mI
Featuring Dr James Grime - https://twitter.com/jamesgrime
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Google Plus: http://bit.ly/numberGplus
Tumblr: http://numberphile.tumblr.com
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
A run-down of Brady's channels: http://bit.ly/bradychannels
- published: 03 Feb 2014
- views: 346801
Blue Science's Matt Pulver: Subquantum Kinetics, Godel's Theorem, & Electrogravitics
Original Interview Posted on May 17th, 2013. Edited and Reposted. This More Concise Version Should Facilitate a Better Listening Experience. Thank You and E...
http://wn.com/Blue_Science's_Matt_Pulver_Subquantum_Kinetics,_Godel's_Theorem,_&_Electrogravitics
Original Interview Posted on May 17th, 2013. Edited and Reposted. This More Concise Version Should Facilitate a Better Listening Experience. Thank You and E...
- published: 22 Sep 2013
- views: 1688
- author: Foks0904
Godel: Key Thinkers at the University of Sydney
- Order: Reorder
- Duration: 3:25
- Updated: 08 May 2014
- author: The University of Sydney
KURT GÖDEL AND THE LIMITS OF MATHEMATICS - Professor Mark Colyvan, Professor of Philosophy and Director of the Sydney Centre for the Foundations of Science K...
http://wn.com/Godel_Key_Thinkers_at_the_University_of_Sydney
KURT GÖDEL AND THE LIMITS OF MATHEMATICS - Professor Mark Colyvan, Professor of Philosophy and Director of the Sydney Centre for the Foundations of Science K...
- published: 21 Oct 2009
- views: 8266
- author: The University of Sydney
Godel Online Lecture 3: Natural Numbers with Successor
- Order: Reorder
- Duration: 29:37
- Updated: 09 Mar 2013
- author: eric pacuit
http://wn.com/Godel_Online_Lecture_3_Natural_Numbers_with_Successor
2) My Godel Incompleteness Theorem Analogy - Explanation of Incompleteness
- Order: Reorder
- Duration: 12:31
- Updated: 24 Aug 2014
- author: Hythloday71
PRIOR VID - 1 1) An Argument to Pyrrho on - Godel Incompleteness Theorem and Philosophy of Mathematics NEXT VID - 3 3) Numbers to Power Zero Definitional Imp...
http://wn.com/2)_My_Godel_Incompleteness_Theorem_Analogy_-_Explanation_of_Incompleteness
PRIOR VID - 1 1) An Argument to Pyrrho on - Godel Incompleteness Theorem and Philosophy of Mathematics NEXT VID - 3 3) Numbers to Power Zero Definitional Imp...
- published: 26 Feb 2013
- views: 2442
- author: Hythloday71
Gödel's Incompleteness Theorem
- Order: Reorder
- Duration: 3:37
- Updated: 27 Aug 2014
- author: Alejandro Vizcarra
Gödel proved that the consistency of arithmetic, or Number Theory, cannot be proved!
http://wn.com/Gödel's_Incompleteness_Theorem
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- published: 15 May 2014
- views: 164
- author: Alejandro Vizcarra
A Trek through 20th Century Mathematics (6/8) - Set Theory, Russell, Gödel
- Order: Reorder
- Duration: 6:15
- Updated: 05 Apr 2013
- author: Science4AllOrg
Learn more on http://www.science4all.org/ Self-Reference: http://www.science4all.org/le-nguyen-hoang/self-reference/ Construction of Numbers: http://www.scie...
http://wn.com/A_Trek_through_20th_Century_Mathematics_(6_8)_-_Set_Theory,_Russell,_Gödel
Learn more on http://www.science4all.org/ Self-Reference: http://www.science4all.org/le-nguyen-hoang/self-reference/ Construction of Numbers: http://www.scie...
- published: 08 Mar 2013
- views: 154
- author: Science4AllOrg
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13:10
Gödel's Incompleteness Theorem Explained Part 1: Formal Systems and Gödel Numbering
Temporary notice: This series is not yet complete. If you'd really like to see it continue...
published: 07 Apr 2014
author: BestThingWorstThing
Gödel's Incompleteness Theorem Explained Part 1: Formal Systems and Gödel Numbering
Gödel's Incompleteness Theorem Explained Part 1: Formal Systems and Gödel Numbering
- published: 07 Apr 2014
- views: 1908
- author: BestThingWorstThing
23:10
Gödel's Incompleteness Theorem Explained Part 3: Introduction to Typographical Number Theory
Thanks to everyone who gave me feedback on part 2! Now it's time to explain how formal sys...
published: 13 Jul 2014
author: BestThingWorstThing
Gödel's Incompleteness Theorem Explained Part 3: Introduction to Typographical Number Theory
Gödel's Incompleteness Theorem Explained Part 3: Introduction to Typographical Number Theory
- published: 13 Jul 2014
- views: 198
- author: BestThingWorstThing
18:35
Gödel's Incompleteness Theorem Explained Part 4: Properties and Relations of Numbers in TNT
Part 4 of 5 in my series on Gödel's Incompleteness Theorem. As always, based heavily on Do...
published: 04 Aug 2014
author: BestThingWorstThing
Gödel's Incompleteness Theorem Explained Part 4: Properties and Relations of Numbers in TNT
Gödel's Incompleteness Theorem Explained Part 4: Properties and Relations of Numbers in TNT
- published: 04 Aug 2014
- views: 75
- author: BestThingWorstThing
10:07
Theory of Computation: Gӧdel Numbers (Part 01)
1) Pairing Functions 2) An example of a pairing function 3) Course web page is at http://v...
published: 14 Apr 2012
author: vkedco
Theory of Computation: Gӧdel Numbers (Part 01)
Theory of Computation: Gӧdel Numbers (Part 01)
- published: 14 Apr 2012
- views: 481
- author: vkedco
50:05
B3. Godel Numbering and Incompleteness
...
published: 20 Dec 2012
author: Per Stinchcombe
B3. Godel Numbering and Incompleteness
B3. Godel Numbering and Incompleteness
- published: 20 Dec 2012
- author: Per Stinchcombe
7:34
Gödel numbering
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and wel...
published: 05 Aug 2015
Gödel numbering
Gödel numbering
- published: 05 Aug 2015
- views: 1
14:34
Secure Data-Transmission through Images using Godel Numbering
Course project for EEL6562....
published: 06 Dec 2012
author: deepak murthy
Secure Data-Transmission through Images using Godel Numbering
Secure Data-Transmission through Images using Godel Numbering
- published: 06 Dec 2012
- views: 53
- author: deepak murthy
2:18
Gödel's Incompleteness Theorems: History, Proofs, Implications
http://thebrooklyninstitute.com/bisr_course/godels-incompleteness-theorems-history-proofs-...
published: 30 Jan 2013
author: ajayc42
Gödel's Incompleteness Theorems: History, Proofs, Implications
Gödel's Incompleteness Theorems: History, Proofs, Implications
- published: 30 Jan 2013
- views: 3262
- author: ajayc42
0:29
Gödel number Meaning
Video shows what Gödel number means. A number uniquely assigned to each symbol, and to eac...
published: 11 May 2015
Gödel number Meaning
Gödel number Meaning
- published: 11 May 2015
- views: 0
15:00
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human...
published: 18 Oct 2011
author: globalbeehive
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
- published: 18 Oct 2011
- views: 107016
- author: globalbeehive
15:00
Kurt Godel: The World's Most Incredible Mind (Part 2 of 3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human...
published: 05 Nov 2011
author: globalbeehive
Kurt Godel: The World's Most Incredible Mind (Part 2 of 3)
Kurt Godel: The World's Most Incredible Mind (Part 2 of 3)
- published: 05 Nov 2011
- views: 40806
- author: globalbeehive
14:55
Kurt Godel: The World's Most Incredible Mind (Part 3 of 3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human...
published: 10 Nov 2011
author: globalbeehive
Kurt Godel: The World's Most Incredible Mind (Part 3 of 3)
Kurt Godel: The World's Most Incredible Mind (Part 3 of 3)
- published: 10 Nov 2011
- views: 16970
- author: globalbeehive
photo: AP / Alexander Zemlianichenko
15 Sep 2015
(CNN)The Russian military appears to be attempting to set up a forward operating base in western Syria, the U.S. government says, deepening concerns about Moscow's intentions in the war-torn nation. "We have seen indication in recent days that Russia has moved people and things into the area around Latakia, and the airbase there," Pentagon spokesman Capt. Jeff Davis said Monday ... Kerry's warning to Lavrov. Last week, U.S ... JUST WATCHED ... U.S ... ....
photo: AP / Matt Sayles/Invision/
15 Sep 2015
In the blockbuster dinosaur sequel a mobile phone magically fixes itself and Chris Pratt talks to Bryce Dallas Howard without moving his lips. @BenChildGeek. Dinosaur blockbuster Jurassic World features more errors than any other film released so far in 2015, according to the Movie Mistakes website ... Fury Road, with eight mistakes each ... Twitter ... ....
photo: AP / Xinhua, Wang Wei, FILE
15 Sep 2015
By Jack Kim and Ju-min Park. SEOUL (Reuters) - North Korea said on Tuesday its main nuclear complex was operating and it was working to improve the "quality and quantity" of its weapons which it could use against the United States at "any time". The comments follow a declaration by the North in 2013 vowing to restart all nuclear facilities, including the main nuclear reactor in Yongbyon that had been shuttered....
photo: Via YoutTube
14 Sep 2015
Two topless feminist protesters from Femen have stormed the stage of a conference discussing women in Islam. A video of the incident appears to show one of the activists being kicked by a man as she is hauled off stage at the event in France. The two women are from the Femen activist group, whose members are known for protesting topless with writing across their chest ... The so-far unnamed women are believed to be aged 25 and 31 ... --> ... ....
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noodls
23 Jun 2014
In a similar way, a number can be assigned to any mathematical statement - the so called "Gödel number" ... But this way, sentences can be constructed which are not only statements about numbers, but statements about mathematical formulas - such as "n is not the Gödel number of a proof of the statement F" - and this statement itself can again be coded with a Gödel number....
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