I didn't expect it to actually be an easy proof. In Wikipedia all of the proofs are complicated and I just quit trying to understand them. But this is so simple! Made my day :)
Okay this was insightful , it's not very immediately visible that the series would diverge and understandably so. Subscribed and requesting you for more of these , thank you!
Thanks for the kind comments! I am actually in the process of starting a new math TH-cam channel separate from this one, which I really began 3 years ago to use in my own classes during the pandemic. The first project I have in mind is to make a complete set of videos on introduction to proofs, what is usually called "Transition to higher math" or "Introduction to set theory and logic". After that, who knows -- maybe some number theory, abstract algebra, complex analysis... And of course other standalone videos. It seems for a lot of these more advanced topics, there are some excellent isolated videos, but few that cover the material comprehensively and in detail, as you would get from a college class. When the new channel is ready to go, I'll make an announcement here!
This is really well presented and I understood it the first time through. I see almost all your other videos are too advanced for me but I look forward to checking out some of the more basic ones.
Thanks a ton. This is in Apostol's Analytic Number Theory Chapter 1 (also referenced to Clarkson, which is how I found this video!) and I was having trouble understanding it. The example really helped!
"it diverges on the order of the log of the log" So, there exists something analogous to the Euler Mascheroni constant - the limit of the difference of this sum going to n and the log of the log of n, for n going to infinity?
OK, this proof has gained popularity over the years and is visible in may vidéos. A more complicated challenge : what if we supress from th sum all prime(i) that contain a "1" ? Idem with a "2" ? The same until 9 ? Anybody interested with this amazing problem ?
That is an interesting question! I would have to think about it a bit. My intuition is that even suppressing any single decimal digit, the sum would still diverge.
Of course, that's a great proof. I don't know if I'd call it easier, though, because you have to know Taylor series, and all this requires is knowledge of geometric series and the harmonic series.
I didn't expect it to actually be an easy proof. In Wikipedia all of the proofs are complicated and I just quit trying to understand them. But this is so simple! Made my day :)
Okay this was insightful , it's not very immediately visible that the series would diverge and understandably so. Subscribed and requesting you for more of these , thank you!
Thanks for the kind comments!
I am actually in the process of starting a new math TH-cam channel separate from this one, which I really began 3 years ago to use in my own classes during the pandemic. The first project I have in mind is to make a complete set of videos on introduction to proofs, what is usually called "Transition to higher math" or "Introduction to set theory and logic".
After that, who knows -- maybe some number theory, abstract algebra, complex analysis... And of course other standalone videos. It seems for a lot of these more advanced topics, there are some excellent isolated videos, but few that cover the material comprehensively and in detail, as you would get from a college class.
When the new channel is ready to go, I'll make an announcement here!
This is really well presented and I understood it the first time through. I see almost all your other videos are too advanced for me but I look forward to checking out some of the more basic ones.
This is a very satisfying proof indeed.
I have known the Clarkson's proof for some time.
This is a very very nice improvement.
Glad you liked it!
Very cool and simple proof of this nice statement. It implies that there are quite many primes that are greater or equal to any natural number :)
That really hurt my head but I did appreciate it! 🙂
Thanks a ton. This is in Apostol's Analytic Number Theory Chapter 1 (also referenced to Clarkson, which is how I found this video!) and I was having trouble understanding it. The example really helped!
Glad you found it helpful. Apostol's book is actually how I found that paper.
Impressive! Really nice content, l'm waiting for the next videos❤️
Thank you! I'm actually working on starting up a separate math channel from this one. I will make an announcement when it's closer to launch.
"it diverges on the order of the log of the log"
So, there exists something analogous to the Euler Mascheroni constant - the limit of the difference of this sum going to n and the log of the log of n, for n going to infinity?
Yes, look up Meissel-Mertens constant. The value is approximately 0.2615.
@@DarinBrownSJDCMath Thanks! :)
cool proof well presented
Beautiful proof. Thank you.
OK, this proof has gained popularity over the years and is visible in may vidéos.
A more complicated challenge : what if we supress from th sum all prime(i) that contain a "1" ? Idem with a "2" ? The same until 9 ? Anybody interested with this amazing problem ?
That is an interesting question! I would have to think about it a bit. My intuition is that even suppressing any single decimal digit, the sum would still diverge.
beautiful
I find Erdos's proof easier to follow.
Nice!
This is genius
It is much easier with Taylor expansion...
Of course, that's a great proof. I don't know if I'd call it easier, though, because you have to know Taylor series, and all this requires is knowledge of geometric series and the harmonic series.
I can count to three.