Start Learning Reals 1 | Cauchy Sequences
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- เผยแพร่เมื่อ 13 ต.ค. 2024
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This is my video series about Start Learning Sets. We discuss basic definition, like union and intersection, and also go into the details of maps and functions. I hope that it will help everyone who wants to learn about it.
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I hope that this helps students, pupils and others. Have fun!
(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start
![Start Learning Reals 2 | Completeness Axiom [dark version]](http://i.ytimg.com/vi/aidZPdDR-q4/mqdefault.jpg)
![Start Learning Reals 2 | Completeness Axiom [dark version]](/img/tr.png)
If a video is good, you might be jealous and don't want to share it. But these videos are not "good" anymore, they are fantastic and wonderful, something beyond good, making it a shame not to share them. Thank you for making these great videos, sir, I really can't show more my appreciations.
Thanks :) And please share as much as you can!
Thank you for these awesome videos. They're such awesome bite-size chunks. I really struggled so much with understanding these fundamentals years back when I just started uni I felt so overwhelmed back then. But these videos are just perfect. A second chance.Thank you!
You are so welcome!
Nice, I'm excited for this. I never understood the construction of the Reals as well as I would like.
Sir please continue this series
I really appreciate your videos. I would love to see some very rigorous probability theory if you have time. I am not sure what topic it is called.
After watching the first video, I really have a good feeling that this channel will help me understand maths!
Thank you very much :)
This is extremely useful and precise, i'm following your videos and trying to formalize this with a proof assistant (Agda) and i mechanize all this thanks of this videos being somewhat formal already. Thanks.
Glad it was helpful! :)
I subscribed! I'm going to watch your other videos, I'm a computer scientist so don't really know about much more than discrete maths. Greetings from Argentina!@@brightsideofmaths
Amazing video for understanding the construction of the reals with the cantor method comparing to the traditional dedekind cut method
Thank you very much :)
Very nice presentation..thanks for uploading..
I love it!
Everything in this channel is fantastic, thanks!
But, as a non mathematician, I wonder why we need something like Cauchy series o Dedekind cuts in a math course, if we all agree the existence of irrational numbers is axiomatic...
The existence is a consequence of the axioms. That's why we need Cauchy sequences and so on.
Great video!
Just one question: when you mention that one can pick any small section of the line where the distance from left to right is just given by epsilon and only finitely many points would lie outside, this epsilon interval must have at its center the limit point of the sequence, right? Because I don't see that applicable if I pick a small epsilon interval around x_1 for instance.
The center is not so important. It's important that the limit point lies inside :)
Thank you very much! Your channel is brilliant and extremely useful
I want to share another definition for absolute value that I saw in an Analysis book. |x| = max(x, -x). I think this definition is much eleganter.
Sure, this is also possible :)
I love your videos!! You probably single handedly handed my degree to me
Thank you very much :)
*angry wildberger sounds*