Відео

only video I could find that showed this

I was asked on an interview, what is equation of a line, I said slope equals rise over run, they said wrong, y=mx+b.

Nice

Thank you Dr. Marrero!

thanks

I failed pre cal but this video was pretty cool

Very good explanation,

How did you get a negative

🎉

p1 + p2 = 2(n + m) ∀n∈Z+, n>2

D

That's what's known as a "removable discontinuity"!

is there a way to prove that every 4th sequence is divisible by 3

I thought you are going to show on the second problem that the answer is simply 8 x 3 = 24 (9x+6) is 3 times (3x+2)

24

24

Thanks ❤

I really like your way of solving exercises. ❤❤❤

Thanks for teaching❤❤❤

You are the greatest teacher of the all time ❤❤❤

Respected sir, I have to say, your teaching statergy blows my mind. You're one of those rarest teachers that really *teaches* the student instead of just telling the answer. I request you to always smile ahead in your life and never stop teaching us. Thank you alot

the last one really good

1. there is no operation to find a root. 2. To find a root you have to estimate a number, square it, and see if it the square root of the number you are looking for. 3. So, the square root of two cannot be 2 and cannot be 1. Therefore, it is a fraction between 1 and two. 4. However, we don't actually square fractions. What we do is turn them into rational numbers and iterate through possibilities, looking for them. 5. Here's how we do that. So we choose 1.1 We then turn that into 11/10. We then square it 11/10 x 11/10 6. So what we are really doing is squareing the 11s and then the 10s. We end up with 121/100. 7. We then reduce back down. 1.21 8. Because the denominator is squared to, fractions do not create squares that are that much larger. This is kind of a noticeable thing. Now you know why. 9. But the result is that 1.1 squared is 1.21 10. So, not the square root of 2, right? 11. So, we would keep iterating, trying to get closer. 12. They key here is that the truth is that we can only create perfect squares this way. And then reduce them back. 13. But unfortunately, there is no perfect square that reduces back to 2. There is some math proof to this. Basically, it's a "rectangular" ratio. 14. At any rate, so what we do is we create a perfect square that is just less than it. And one that is just a little bit more than it. And while these numbers can eternally get closer, they are never right on. Now, let's get to the philosophy of it. Why can't we calculate the diagonal of a damned square? 1How can a perfect square... the basis of all math... not have a diagonal that is calculable? So, here is the truth. Because perfect squares do not exist in the physical world either! Lol. Big metaphysical secret. If you make a perfect square in the physical world, the diagonal length 'vibrates'. It oscillates to some degree. All irrational numbers can be visualized to do this. Imagine the measures vibrating back and forth a bit, like a vibrating guitar string. Now, this might seem ridiculous or impossible. But math actually models physical reality. Look around you. See how there are nodes and antinodes? Things that are still and things that are moving? There you go. It's in the math. Always has been. The only reason this seems so strange is because we're taught differently. Another aspect of this, is if you set the diagonal length to "1", then the SIDES of the square become irrational. So this starts getting into the idea that the observer decides which points are irrational or rational. the whole 'observer' effect we see so clearly in quantum physics. It's very strange, I worked on rational and irrational numbers a long time. But when I finally understood... I could visualize the number line. The rational numbers are solid lengths. The irrational numbers vibrate, depending on the precision. And it actually aligns with reality BETTER. I can choose which lengths are 1 and shift the irrational numbers around like playing chords on a guitar. It makes more sense. Oscillations happen in sine waves. Sine waves happen in spirals. Spiral and spiritual share their root words. So you can think of irrational numbers as being 'spiritual' if you will. All this stuff is right there in math on day 1 of geometry. But they hide it under an ugly root sign because they don't want people to know. Anyway, if you don't think I'm right, that's fine. Maybe I'm wrong. Always room for argument and new information... but once again... look around you. Math models reality. Look at reality. It's vibrating. If you just forget what we've been taught... and open your mind... you will see... math is imprecise, imperfect, approximate, with vibrating numbers and measure... JUST LIKE THE WORLD

9. Goldbach's Conjecture: An Information-Theoretic Perspective 9.1 Background Goldbach's Conjecture states that every even integer n > 2 can be written as the sum of two primes. Despite its simple statement, it has resisted proof for nearly 300 years. 9.2 Information-Theoretic Reformulation Let's reframe the problem in terms of information theory: 9.2.1 Prime Information Content: Define the prime information content of an integer n: I_p(n) = log₂(π(n)) where π(n) is the prime counting function. 9.2.2 Goldbach Decomposition Information: For an even integer n, define: I_G(n) = min{I_p(p) + I_p(n-p) : p prime, p ≤ n/2} 9.2.3 Goldbach Conjecture as Information Statement: Reformulate Goldbach's Conjecture as: ∀n > 2, n even: I_G(n) < I_p(n) 9.3 Information-Theoretic Conjectures 9.3.1 Information Conservation in Goldbach Pairs: For most even n, I_p(p) + I_p(n-p) ≈ I_p(n) for Goldbach pairs (p, n-p). 9.3.2 Goldbach Information Spectrum: The spectrum of I_G(n) values has specific structural properties related to the distribution of primes. 9.3.3 Information Efficiency of Goldbach Decompositions: Goldbach decompositions represent efficient ways of encoding even integers using prime information. 9.4 Analytical Approaches 9.4.1 Information Entropy of Goldbach Partitions: Study the entropy of the distribution of Goldbach partitions for a given even integer. 9.4.2 Prime Information Flow: Model the "flow" of prime information in Goldbach decompositions as n increases. 9.4.3 Information-Theoretic Sieve Methods: Develop sieve methods based on information-theoretic principles to study Goldbach partitions. 9.5 Computational Approaches 9.5.1 Quantum Algorithms for Goldbach Decompositions: Develop quantum algorithms for finding and analyzing Goldbach partitions. 9.5.2 Machine Learning for Prime Pattern Recognition: Train neural networks to recognize patterns in the information structure of Goldbach partitions. 9.5.3 Information-Based Prime Generation: Create algorithms for generating primes optimized for Goldbach decompositions. 9.6 Potential Proof Strategies 9.6.1 Information Inequality Approach: Prove that I_G(n) < I_p(n) for all even n > 2 using information-theoretic inequalities. 9.6.2 Asymptotic Information Analysis: Show that lim_{n→∞} (I_p(n) - I_G(n)) = ∞, implying the conjecture for sufficiently large n. 9.6.3 Information-Theoretic Induction: Develop a form of induction based on information content to prove the conjecture for all n. 9.7 Immediate Next Steps 9.7.1 Rigorous Formalization: Develop a mathematically rigorous formulation of the information-theoretic concepts introduced. 9.7.2 Computational Experiments: Conduct extensive numerical studies on the information properties of Goldbach partitions. 9.7.3 Interdisciplinary Collaboration: Engage experts in number theory, information theory, and quantum computing to refine these ideas. 9.8 Detailed Plan for Immediate Action 9.8.1 Mathematical Framework Development: - Rigorously define I_p(n) and I_G(n) and prove their basic properties - Establish formal relationships between these information measures and classical results on Goldbach's Conjecture - Develop an information-theoretic version of the circle method for studying Goldbach partitions 9.8.2 Computational Modeling: - Implement efficient algorithms for computing I_p(n) and I_G(n) for large n - Create visualizations of the "information landscape" of Goldbach partitions - Develop machine learning models to predict properties of Goldbach decompositions 9.8.3 Analytical Investigations: - Study the statistical properties of I_G(n) as n varies - Investigate connections between I_G(n) and other number-theoretic functions - Analyze the information-theoretic properties of exceptional sets in Goldbach-type problems 9.8.4 Quantum Approaches: - Develop quantum algorithms for efficiently computing Goldbach partitions - Investigate if quantum superposition can be used to analyze multiple Goldbach partitions simultaneously - Explore quantum annealing techniques for optimizing Goldbach decompositions 9.9 Advanced Theoretical Concepts 9.9.1 Information Topology of Prime Patterns: - Define a topology on the space of prime patterns based on their information content - Study how Goldbach partitions relate to the geometric properties of this space 9.9.2 Goldbach Flows in Information Space: - Model Goldbach partitions as flows in an abstract information space - Investigate if techniques from dynamical systems can be applied to these flows 9.9.3 Quantum Prime States: - Develop a quantum mechanical model of prime numbers where primes exist in superposition - Explore how measuring these quantum prime states relates to Goldbach partitions 9.10 Long-term Vision Our information-theoretic approach to Goldbach's Conjecture has the potential to: 1. Provide new insights into the distribution of primes and their additive properties 2. Offer a fresh perspective on other major conjectures in additive number theory 3. Bridge concepts from information theory, quantum computing, and number theory 4. Suggest new computational approaches to number-theoretic problems By pursuing this multifaceted approach, we maximize our chances of making significant progress on this longstanding problem. Even if we don't immediately prove the conjecture, this approach promises to yield valuable new insights into the nature of primes and their information content.

Great🎉thank you

Sry can that mouse be a bit bigger? I couldn't find it

Sry can that mouse be a bit bigger? I couldn't find it

Thanks sir you really explained functions very well..

Thank you sir ! I will take it on saturday so this was really helpful

If twenty one dollars are charged for the first twenty-five people then multiply those two numbers to get five hundred and twenty-five. Then, plug in twenty-five for n in the answer choices which will result in only a giving the correct answer.

Thank you sir. Love to know more on history of mathematics.

I love your Videos Dr.!!!! Please can you do more on triangles?

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Great video as usual 0:21

Excellent 6:33

0:13 thank you for sharing 🎉

Thank you for doing this; the nonsensensical output from a simple reasoning test like this reveals glaring limitations of chat-bot technology, amongst its clearly amazing capabilities and growing hype!