Theory of computation | Algorithmic information theory | Real transcendental numbers

Chaitin's constant

In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin. Although there are infinitely many halting probabilities, one for each method of encoding programs, it is common to use the letter Ω to refer to them as if there were only one. Because Ω depends on the program encoding used, it is sometimes called Chaitin's construction when not referring to any specific encoding. Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Each halting probability is Martin-Löf random, meaning there is not even any algorithm which can reliably guess its digits. (Wikipedia).

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The Constant of Integration is ALWAYS Zero

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Constant of Integration is ALWAYS Zero

From playlist Math Magic

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The Euler Mascheroni Constant

I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is

From playlist Series

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How an Equilibrium Constant varies with Temperature - Thermodynamics - Physical Chemistry

Deriving a quantitative relationship to show how an equilibrium constant varies with temperature and so showing were Le Chatelier's Principle comes from in this context. Along the way, the Gibbs-Helmholtz van't Hoff equations are derived and used. My video for deriving the thermodynamics

From playlist Introductory Thermodynamics

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The limit is the limit is the limit is the limit

Here I evaluate a neat infinite limit with l'Hopital's rule... does it work though? Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Instagram: https://www.instagram.com/peyamstagram/ Follow me on Twitter: https

From playlist Calculus

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Max is continuous

In this video, I show a really neat result, namely that the maximum of two continuous functions is continuous. Enjoy the epsilon-delta extravaganza! Continuity Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmB86yhDeAUZPY0dktFtb8Tj Subscribe to my channel: https://youtube.com/d

From playlist Limits and Continuity

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All the Numbers - Numberphile

Matt Parker talks about numbers - as he often does. His book "Humble Pi" is at: http://bit.ly/Humble_Pi More links & stuff in full description below ↓↓↓ The book on Amazon: https://amzn.to/2NKposg Numberphile podcast is on your podcast player. Or the website is: https://www.numberphile.c

From playlist Matt Parker (standupmaths) on Numberphile

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This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language:

From playlist Explore the World Science Festival

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From playlist How is Mathematics Truth and Beauty? - CTT Interview Series

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Gregory Chaitin - Is Mathematics Invented or Discovered?

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From playlist Is Mathematics Invented or Discovered? - CTT Interview Series

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Kolmogorov Complexity - Applied Cryptography

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

From playlist Applied Cryptography

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Identifying constant of proportionality graphically

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From playlist Algebra 1 | Get Ready for Grade Level | Khan Academy

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Gregory Chaitin - What Can Science Say About God?

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From playlist Big Questions About God - Closer To Truth - Core Topic

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From playlist Big Questions About God - Closer To Truth - Core Topic

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From playlist Closer To Truth | Season 4

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Epsilon Delta Continuity (Example 6): 1/x

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From playlist Limits and Continuity

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Maximum and Minimum

Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh

From playlist Real Numbers

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Maximum modulus principle

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From playlist Complex Analysis

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Many people asked me to solve this one! What is the value of x? Many more solutions https://twitter.com/preshtalwalkar/status/1254337151359234049 Solution by Ahmet ÇETİN https://twitter.com/ahmetcet_n/status/1254557842733924354 Subscribe: https://www.youtube.com/user/MindYourDecisions?s

From playlist Math Puzzles, Riddles And Brain Teasers

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From playlist Knowledge

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f/g is continuous

Here I show that the ratio of two continuous functions is continuous. I do it both by using epsilon-delta and the sequence definition of continuity. Interestingly, the proof is similar to the proof of the quotient rule for derivatives. Enjoy! Reciprocals of limits: https://youtu.be/eRs84C

From playlist Limits and Continuity

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