Start Learning Reals - Part 1 - Cauchy Sequences

Thanks to all supporters! They are mentioned in the credits of the video :)

This is my video series about Start Learning Reals. I hope that it will help everyone who wants to learn about it.

#StartLearningReals

This video is about the start learning mathematics. Here, we discuss Cauchy sequences of rational numbers. These will be very important when we want to construct the real numbers.

I hope that this helps students, pupils and others.

#StartLearningMathematics #Numbers

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[maohejiang]

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.

[zombieboobuu]

After watching the first video, I really have a good feeling that this channel will help me understand maths!

[nawalmc]

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!

[zazinjozaza]

Nice, I'm excited for this. I never understood the construction of the Reals as well as I would like.

[JDMathematicsAndDataScience]

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.

[一一-yc]

Amazing video for understanding the construction of the reals with the cantor method comparing to the traditional dedekind cut method

[pebotin]

Very nice presentation..thanks for uploading..

[juansalvadordomandl]

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.

[budokan]

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.

[doncney]

I love your videos!! You probably single handedly handed my degree to me

[marcocenci]

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...

[ahmedamr]

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.