Banach Fixed-Point Theorem [dark version]

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This is my video series about Multivariable Calculus also known as Analysis with more variables or in higher dimensions. I hope that it will help everyone who wants to learn about it. We discuss partial derivatives, the nabla operator, gradient, Jacobians, Hessian, and so on. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/com...
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[@Hold_it]

I might have already seen the bright version, but a second time might not hurt :D

[@etcd]

I've been fascinated by fixed points in functions after I self-(re)discovered the Riemann Zeta function's real value fixed point (OEIS A069995). Love the channel and the video, please keep up the great work!

[@DitDitDitDahDahDahDitDitDit]

In all these proofs re completeness that rely on the notion of sequences being convergent within the boundaries of some generalized blob, as in the one started here around 7.5 minutes, drawing dots and talking about “all sequences” always goes right over my poor head. There’s not enough detail for my apparently mathematically under-developed mind. Please point me to where I can learn what sequences we are talking about, and, perhaps, examples of sequences that are excluded. This basic idea is eluding me. Thank you for all these beautiful lectures.

[@brightsideofmaths]

I have a Real Analysis course where you can learn all this and more :)

[@DitDitDitDahDahDahDitDitDit]

I’ve looked at your real analysis series and my problem appears to be that when one refers generically to “series” being convergent within, my bad pun, “the blob” shape, I don’t know what those implicated series are or where they come from. It’s one thing to pick a series and study its characteristics, as most of the RA videos do. I seem to miss an appreciation of how I should see those principles applying in this particular video. Perhaps it might illuminate my ignorance (there’s an incompatibility of terms) by asking for examples of appropriate series that fit such invocations. Anyway, thanks for the wonderful videos, and I really ought not to waste any more of your time. Struggling to understand new concepts is part of the fun.

[@satiremuch2643]

What if the distance is 0.9999... + 0.0000...1. How far away are they then (if the lights are turned off)? 1:54

[@brightsideofmaths]

What?

[@satiremuch2643]

@@brightsideofmaths Well this is the dark version, if I'm not mistaken, is it not?