- published: 01 Jun 2020
- views: 1312106
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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.
Simplified overview
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 - https://wn.com/Gödel_numbering
Podcasts:
-
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
good explanation from his interview with joe rogan https://www.youtube.com/watch?v=GEw0ePZUMHA
published: 01 Jun 2020 -
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Conn...
published: 20 Jul 2021 -
Gödel's Incompleteness Theorem in 90 Seconds!
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to understand, but trying to explain it in 90 seconds is a whole lot tougher. I hope that my speed run of this is coherent and can maybe help you understand the topic! This video is for the #breakthroughjuniorchallenge
published: 26 Jun 2022 -
Gödel's Incompleteness (extra footage 1) - Numberphile
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc More links & stuff in full description below ↓↓↓ Extra footage part 2: https://youtu.be/7DtzChPqUAw Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy's book as mentioned... In the US it is called The Great Unknown - http://amzn.to/2sfkWpb In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp More of his books: http://amzn.to/2ryEk4r Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphil...
published: 03 Jun 2017 -
The simplest version of Godel's theorem and why it's important
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-knowing computer (the limits of the thinking mind) that it can state any truth. Let's call it UTM for universal truth machine. Now if we write out G="UTM will never say G is true" and then ask UTM if G is true, we have put it to its limit. UTM cannot say it is true....which makes it true! The proves the limits of thinking and how there are truths beyond thinking.
published: 07 May 2022 -
Gödel's Incompleteness Theorem - Numberphile
Marcus du Sautoy discusses Gödel's Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy's book as mentioned... In the US it is called The Great Unknown - http://amzn.to/2sfkWpb In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp More of his books: http://amzn.to/2ryEk4r Discuss this one on Brady's subreddit: https://redd.it/6eet91 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simo...
published: 31 May 2017 -
megafavnumber - Gödel Encoding
#megafavnumber I don't really have a favorite number over 1,000,000. On the other hand, I do have a favorite process that will often produce very large numbers.
published: 30 Aug 2020 -
Cracking the Code: Understanding Gödel's Theorem in Mathematics #shorts
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematics. Join us as we explore the limits of proof and delve into famous unsolved problems like Fermat's Last Theorem and the Goldbach conjecture. Uncover the mysteries of numbers and their elusive truths. #GödelTheorem #Mathematics #Proofs #FermatsLastTheorem #GoldbachConjecture #Numbers #UnsolvedProblems #MathematicalTruths #NumberTheory #MathEnthusiasts
published: 28 Feb 2024 -
Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths
published: 08 Jun 2023 -
The Gödel incompleteness phenomenon
Joel David Hamkins, Professor of Logic, Oxford University This lecture is based on chapter 7 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press, https://mitpress.mit.edu/books/lectures-philosophy-mathematics. Chapter 7. Incompleteness David Hilbert sought to secure the consistency of higher mathematics by finitary reasoning about the formalism underlying it, but his program was dashed by Gödel’s incompleteness theorems, which show that no consistent formal system can prove even its own consistency, let alone the consistency of a higher system. We shall describe several proofs of the first incompleteness theorem, via the halting problem, self-reference, and definability, showing senses in which we cannot complete mathematics. After this, we shall discuss the ...
published: 25 Nov 2020
developed with YouTube
3:39
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
- Order: Reorder
- Duration: 3:39
- Uploaded Date: 01 Jun 2020
- views: 1312106
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0ePZUMHA
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0ePZUMHA
https://wn.com/Roger_Penrose_Explains_Godel's_Incompleteness_Theorem_In_3_Minutes
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0ePZUMHA
5:20
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
- Order: Reorder
- Duration: 5:20
- Uploaded Date: 20 Jul 2021
- views: 3835870
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.
--
Consider the following sentence: “...
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.
--
Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem.
Lesson by Marcus du Sautoy, directed by BASA.
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View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy
Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper
Animator's website: https://basaestudio.com
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Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.
https://wn.com/The_Paradox_At_The_Heart_Of_Mathematics_Gödel's_Incompleteness_Theorem_Marcus_Du_Sautoy
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.
--
Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem.
Lesson by Marcus du Sautoy, directed by BASA.
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View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy
Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper
Animator's website: https://basaestudio.com
----------------------------------------------
Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.
- published: 20 Jul 2021
- views: 3835870
1:30
Gödel's Incompleteness Theorem in 90 Seconds!
- Order: Reorder
- Duration: 1:30
- Uploaded Date: 26 Jun 2022
- views: 30207
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to understand, but trying to explain it in 90 seconds is a whole lot tougher. ...
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to understand, but trying to explain it in 90 seconds is a whole lot tougher. I hope that my speed run of this is coherent and can maybe help you understand the topic!
This video is for the #breakthroughjuniorchallenge
https://wn.com/Gödel's_Incompleteness_Theorem_In_90_Seconds
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to understand, but trying to explain it in 90 seconds is a whole lot tougher. I hope that my speed run of this is coherent and can maybe help you understand the topic!
This video is for the #breakthroughjuniorchallenge
- published: 26 Jun 2022
- views: 30207
13:24
Gödel's Incompleteness (extra footage 1) - Numberphile
- Order: Reorder
- Duration: 13:24
- Uploaded Date: 03 Jun 2017
- views: 374028
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc
More links & stuff in full description below ↓↓↓
Extra footage part 2: https://youtu.be/7DtzChPqUAw
Professor Marcus ...
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc
More links & stuff in full description below ↓↓↓
Extra footage part 2: https://youtu.be/7DtzChPqUAw
Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
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Numberphile tweets: https://twitter.com/numberphile
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Sign up for (occasional) emails: http://eepurl.com/YdjL9
https://wn.com/Gödel's_Incompleteness_(Extra_Footage_1)_Numberphile
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc
More links & stuff in full description below ↓↓↓
Extra footage part 2: https://youtu.be/7DtzChPqUAw
Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
- published: 03 Jun 2017
- views: 374028
5:33
The simplest version of Godel's theorem and why it's important
- Order: Reorder
- Duration: 5:33
- Uploaded Date: 07 May 2022
- views: 25814
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-knowing computer (the limits of the thinking mind) that it can state any...
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-knowing computer (the limits of the thinking mind) that it can state any truth. Let's call it UTM for universal truth machine. Now if we write out G="UTM will never say G is true" and then ask UTM if G is true, we have put it to its limit. UTM cannot say it is true....which makes it true! The proves the limits of thinking and how there are truths beyond thinking.
https://wn.com/The_Simplest_Version_Of_Godel's_Theorem_And_Why_It's_Important
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-knowing computer (the limits of the thinking mind) that it can state any truth. Let's call it UTM for universal truth machine. Now if we write out G="UTM will never say G is true" and then ask UTM if G is true, we have put it to its limit. UTM cannot say it is true....which makes it true! The proves the limits of thinking and how there are truths beyond thinking.
- published: 07 May 2022
- views: 25814
13:52
Gödel's Incompleteness Theorem - Numberphile
- Order: Reorder
- Duration: 13:52
- Uploaded Date: 31 May 2017
- views: 2248550
Marcus du Sautoy discusses Gödel's Incompleteness Theorem
More links & stuff in full description below ↓↓↓
Extra Footage Part One: https://youtu.be/mccoBBf0VDM...
Marcus du Sautoy discusses Gödel's Incompleteness Theorem
More links & stuff in full description below ↓↓↓
Extra Footage Part One: https://youtu.be/mccoBBf0VDM
Extra Footage Part Two: https://youtu.be/7DtzChPqUAw
Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Discuss this one on Brady's subreddit: https://redd.it/6eet91
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Animation in this video by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
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Sign up for (occasional) emails: http://eepurl.com/YdjL9
https://wn.com/Gödel's_Incompleteness_Theorem_Numberphile
Marcus du Sautoy discusses Gödel's Incompleteness Theorem
More links & stuff in full description below ↓↓↓
Extra Footage Part One: https://youtu.be/mccoBBf0VDM
Extra Footage Part Two: https://youtu.be/7DtzChPqUAw
Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Discuss this one on Brady's subreddit: https://redd.it/6eet91
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Animation in this video by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
- published: 31 May 2017
- views: 2248550
8:14
megafavnumber - Gödel Encoding
- Order: Reorder
- Duration: 8:14
- Uploaded Date: 30 Aug 2020
- views: 839
#megafavnumber
I don't really have a favorite number over 1,000,000. On the other hand, I do have a favorite process that will often produce very large numbers...
#megafavnumber
I don't really have a favorite number over 1,000,000. On the other hand, I do have a favorite process that will often produce very large numbers.
https://wn.com/Megafavnumber_Gödel_Encoding
#megafavnumber
I don't really have a favorite number over 1,000,000. On the other hand, I do have a favorite process that will often produce very large numbers.
- published: 30 Aug 2020
- views: 839
0:52
Cracking the Code: Understanding Gödel's Theorem in Mathematics #shorts
- Order: Reorder
- Duration: 0:52
- Uploaded Date: 28 Feb 2024
- views: 100
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematics. Join us as we explore the limits of proof and delve into famous uns...
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematics. Join us as we explore the limits of proof and delve into famous unsolved problems like Fermat's Last Theorem and the Goldbach conjecture. Uncover the mysteries of numbers and their elusive truths. #GödelTheorem #Mathematics #Proofs #FermatsLastTheorem #GoldbachConjecture #Numbers #UnsolvedProblems #MathematicalTruths #NumberTheory #MathEnthusiasts
https://wn.com/Cracking_The_Code_Understanding_Gödel's_Theorem_In_Mathematics_Shorts
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematics. Join us as we explore the limits of proof and delve into famous unsolved problems like Fermat's Last Theorem and the Goldbach conjecture. Uncover the mysteries of numbers and their elusive truths. #GödelTheorem #Mathematics #Proofs #FermatsLastTheorem #GoldbachConjecture #Numbers #UnsolvedProblems #MathematicalTruths #NumberTheory #MathEnthusiasts
- published: 28 Feb 2024
- views: 100
0:38
Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths
- Order: Reorder
- Duration: 0:38
- Uploaded Date: 08 Jun 2023
- views: 789828
- published: 08 Jun 2023
- views: 789828
1:19:48
The Gödel incompleteness phenomenon
- Order: Reorder
- Duration: 1:19:48
- Uploaded Date: 25 Nov 2020
- views: 18448
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 7 of my book, Lectures on the Philosophy of Mathematics, published wi...
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 7 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press, https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Chapter 7. Incompleteness
David Hilbert sought to secure the consistency of higher mathematics by finitary reasoning about the formalism underlying it, but his program was dashed by Gödel’s incompleteness theorems, which show that no consistent formal system can prove even its own consistency, let alone the consistency of a higher system. We shall describe several proofs of the first incompleteness theorem, via the halting problem, self-reference, and definability, showing senses in which we cannot complete mathematics. After this, we shall discuss the second incompleteness theorem, the Rosser variation, and Tarski’s theorem on the nondefinability of truth. Ultimately, one is led to the inherent hierarchy of consistency strength rising above every foundational mathematical theory.
https://wn.com/The_Gödel_Incompleteness_Phenomenon
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 7 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press, https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Chapter 7. Incompleteness
David Hilbert sought to secure the consistency of higher mathematics by finitary reasoning about the formalism underlying it, but his program was dashed by Gödel’s incompleteness theorems, which show that no consistent formal system can prove even its own consistency, let alone the consistency of a higher system. We shall describe several proofs of the first incompleteness theorem, via the halting problem, self-reference, and definability, showing senses in which we cannot complete mathematics. After this, we shall discuss the second incompleteness theorem, the Rosser variation, and Tarski’s theorem on the nondefinability of truth. Ultimately, one is led to the inherent hierarchy of consistency strength rising above every foundational mathematical theory.
- published: 25 Nov 2020
- views: 18448
3:39
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0eP...
published: 01 Jun 2020
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
- Report rights infringement
- published: 01 Jun 2020
- views: 1312106
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0ePZUMHA
5:20
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathe...
published: 20 Jul 2021
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
- Report rights infringement
- published: 20 Jul 2021
- views: 3835870
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.
--
Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem.
Lesson by Marcus du Sautoy, directed by BASA.
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View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy
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1:30
Gödel's Incompleteness Theorem in 90 Seconds!
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to under...
published: 26 Jun 2022
Gödel's Incompleteness Theorem in 90 Seconds!
Gödel's Incompleteness Theorem in 90 Seconds!
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- published: 26 Jun 2022
- views: 30207
It's Gödels all the way down... Gödel's Incompleteness Theorem is a tough concept to understand, but trying to explain it in 90 seconds is a whole lot tougher. I hope that my speed run of this is coherent and can maybe help you understand the topic!
This video is for the #breakthroughjuniorchallenge
13:24
Gödel's Incompleteness (extra footage 1) - Numberphile
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc
More links & stuff in full description below ↓↓↓
...
published: 03 Jun 2017
Gödel's Incompleteness (extra footage 1) - Numberphile
Gödel's Incompleteness (extra footage 1) - Numberphile
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- published: 03 Jun 2017
- views: 374028
MAIN VIDEO: https://youtu.be/O4ndIDcDSGc
More links & stuff in full description below ↓↓↓
Extra footage part 2: https://youtu.be/7DtzChPqUAw
Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
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5:33
The simplest version of Godel's theorem and why it's important
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-kn...
published: 07 May 2022
The simplest version of Godel's theorem and why it's important
The simplest version of Godel's theorem and why it's important
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- published: 07 May 2022
- views: 25814
In this video I will show you the simplest way to "get" Godel's theorem. Imagine an all-knowing computer (the limits of the thinking mind) that it can state any truth. Let's call it UTM for universal truth machine. Now if we write out G="UTM will never say G is true" and then ask UTM if G is true, we have put it to its limit. UTM cannot say it is true....which makes it true! The proves the limits of thinking and how there are truths beyond thinking.
13:52
Gödel's Incompleteness Theorem - Numberphile
Marcus du Sautoy discusses Gödel's Incompleteness Theorem
More links & stuff in full descr...
published: 31 May 2017
Gödel's Incompleteness Theorem - Numberphile
Gödel's Incompleteness Theorem - Numberphile
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- published: 31 May 2017
- views: 2248550
Marcus du Sautoy discusses Gödel's Incompleteness Theorem
More links & stuff in full description below ↓↓↓
Extra Footage Part One: https://youtu.be/mccoBBf0VDM
Extra Footage Part Two: https://youtu.be/7DtzChPqUAw
Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Professor du Sautoy's book as mentioned...
In the US it is called The Great Unknown - http://amzn.to/2sfkWpb
In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp
More of his books: http://amzn.to/2ryEk4r
Discuss this one on Brady's subreddit: https://redd.it/6eet91
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Animation in this video by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
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Brady's latest videos across all channels: http://www.bradyharanblog.com/
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8:14
megafavnumber - Gödel Encoding
#megafavnumber
I don't really have a favorite number over 1,000,000. On the other hand, I...
published: 30 Aug 2020
megafavnumber - Gödel Encoding
megafavnumber - Gödel Encoding
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- published: 30 Aug 2020
- views: 839
#megafavnumber
I don't really have a favorite number over 1,000,000. On the other hand, I do have a favorite process that will often produce very large numbers.
0:52
Cracking the Code: Understanding Gödel's Theorem in Mathematics #shorts
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematic...
published: 28 Feb 2024
Cracking the Code: Understanding Gödel's Theorem in Mathematics #shorts
Cracking the Code: Understanding Gödel's Theorem in Mathematics #shorts
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- published: 28 Feb 2024
- views: 100
Discover the fascinating concept behind Gödel's Theorem and its implications in mathematics. Join us as we explore the limits of proof and delve into famous unsolved problems like Fermat's Last Theorem and the Goldbach conjecture. Uncover the mysteries of numbers and their elusive truths. #GödelTheorem #Mathematics #Proofs #FermatsLastTheorem #GoldbachConjecture #Numbers #UnsolvedProblems #MathematicalTruths #NumberTheory #MathEnthusiasts
0:38
Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths
published: 08 Jun 2023
Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths
Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths
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- published: 08 Jun 2023
- views: 789828
1:19:48
The Gödel incompleteness phenomenon
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter...
published: 25 Nov 2020
The Gödel incompleteness phenomenon
The Gödel incompleteness phenomenon
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- published: 25 Nov 2020
- views: 18448
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 7 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press, https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Chapter 7. Incompleteness
David Hilbert sought to secure the consistency of higher mathematics by finitary reasoning about the formalism underlying it, but his program was dashed by Gödel’s incompleteness theorems, which show that no consistent formal system can prove even its own consistency, let alone the consistency of a higher system. We shall describe several proofs of the first incompleteness theorem, via the halting problem, self-reference, and definability, showing senses in which we cannot complete mathematics. After this, we shall discuss the second incompleteness theorem, the Rosser variation, and Tarski’s theorem on the nondefinability of truth. Ultimately, one is led to the inherent hierarchy of consistency strength rising above every foundational mathematical theory.
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.
Simplified overview
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 - https://wn.com/Gödel_numbering
Roger Penrose explains Godel's incompleteness theo...
The paradox at the heart of mathematics: Gödel's I...
Gödel's Incompleteness Theorem in 90 Seconds!...
Gödel's Incompleteness (extra footage 1) - Numberp...
The simplest version of Godel's theorem and why it...
Gödel's Incompleteness Theorem - Numberphile...
megafavnumber - Gödel Encoding...
Cracking the Code: Understanding Gödel's Theorem i...
Why greatest Mathematicians are not trying to prov...
The Gödel incompleteness phenomenon...
G-Code
by: JuvenileI ain't terrified from nuthin'
I'm young wild crazy and disgustin'
Better watch me cuz I'm coming
With a oven by my stomach
I'm scramblin' for the money
Tape ya up like a mummy
Call ya people and tell 'em
I need 50 for this dummy
I'm runnin' hidin' and duckin'
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Lovin, lyin' and lustin'
Stealin' killin' and rapin
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Get it got it I take it
Watch ya Chevy mister
Move ya purse miss
Cuz I tote heavy pistols
And man they burst quick
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But shit that was yesterday
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That's my G-code
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Get ya glocks in ya gloves
Ride drops on dubs
We gon' live by that
Make the snitches catch a cut
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Hit the block and open up
We gon' die by that
We raised up lookin' at trees and brick walls
Foreign properties and pack some menthals
Got us a fire connect and went off
Got jammed with this broad that rent cars
Wasn't tryin' to change the game, just be in it
Didn't give a fuck if we balled for 3 minutes
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Bitch couldn't talk to us if she wasn't fuckin'
Ya either be bout it or look and keep truckin
Police drew causes and tried to cross lines
We stuck to the code we lived and died by it
If war ever came we held the fort down
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Stayed on point to make some more green
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Nigga had a habit he supplied his own
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Them other motherfuckers fall off the block
24/7 all around the clock
We hustlin of course in the gamblin spot
We had a chance to stop, we still wasn't ready
Shit kept comin' so we made more fetti
Police drew causes and tried to cross lines
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