Theory of computation | Algorithmic information theory | Real transcendental numbers
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).
The Constant of Integration is ALWAYS Zero
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From playlist Math Magic
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
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
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
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
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
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
Gregory Chaitin - How is Mathematics Truth and Beauty?
When mathematicians speak about their craft, why do they use terms of philosophy and art? What is it about mathematics that can penetrate trivial truth and reveal fundamental “Truth?” What are the characteristics of fundamental truth? What is it about mathematics that can elicit the descri
From playlist How is Mathematics Truth and Beauty? - CTT Interview Series
Gregory Chaitin - Is Mathematics Invented or Discovered?
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/376lkKN Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics
From playlist Is Mathematics Invented or Discovered? - CTT Interview Series
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
Identifying constant of proportionality graphically
Identifying constant of proportionality graphically
From playlist Algebra 1 | Get Ready for Grade Level | Khan Academy
Gregory Chaitin - What Can Science Say About God?
Most scientists believe that science can say nothing about God other than to show that there is no need for such a being. Scientists claim that science is quite capable of providing most explanations today and virtually all explanations in the future. Click here to watch more interviews
From playlist Big Questions About God - Closer To Truth - Core Topic
Can Science Talk God? | Episode 711 | Closer To Truth
Some say that science and God are not related. Others, that science describes a world that evidences "God's handiwork," or a world that works just fine without God. Featuring interviews with David Gross, William Dembski, Victor Stenger, Gregory Chaitin, and George Smoot. Season 7, Episode
From playlist Big Questions About God - Closer To Truth - Core Topic
Is Mathematics Invented or Discovered? | Episode 409 | Closer To Truth
Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans-like chisels and hammers and pieces of music? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? F
From playlist Closer To Truth | Season 4
Epsilon Delta Continuity (Example 6): 1/x
In this video, I use the epsilon-delta definition of continuity to show that f(x) = 1/x is continuous. This is a must-see for every calculus lover, enjoy! Continuity Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmB86yhDeAUZPY0dktFtb8Tj Subscribe to my channel: https://youtube
From playlist Limits and Continuity
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
Maximum modulus principle In this video, I talk about the maximum modulus principle, which says that the maximum of the modulus of a complex function is attained on the boundary. I also show that the same thing is true for the real and imaginary parts, and finally I discuss the strong max
From playlist Complex Analysis
Looks Easy But Is Insanely Hard
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
There's more over on Veritasium! "What is NOT Random?": https://www.youtube.com/watch?v=sMb00lz-IfE SOURCES AND MORE BELOW! My twitter: https://twitter.com/tweetsauce My instagram: http://instagram.com/electricpants Generate random numbers using atmospheric noise: http://www.random.org/
From playlist Knowledge
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