Formal construction of the set of all the real numbers.
Download: http://www.olsak.net/mirek/manim/eost/eost12-dedekind-cuts.mp4
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https://www.youtube.com/watch?v=67OHAES5goA
Introduction to set theory and infinity.
I am now releasing the first 7 chapters concerning the naive theory of infinity.
I am still not completely happy about my English but better to release like that than never. Constructive remarks are welcome although I am probably not going to implement them soon (maybe when releasing further chapters).
Source code: https://github.com/mkoconnor/manim
Video download: http://www.olsak.net/mirek/manim/eost/eost01-intro.mp4
Music: Radek Olšák
Animated with Manim, and also largely inspired by other video series by 3Blue1Brown
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https://www.youtube.com/watch?v=mfheE7Bekzs
Porovnávání ordinálních čísel a jejich dvojí role -- typy dobře uspořádaných množin a indexy jejich prvků.
Video download: http://www.olsak.net/mirek/manim/eost/eost05-ordinals-cz.mp4
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https://www.youtube.com/watch?v=rJ72Hy10JSs
Propagační video k semináři, který se konal v ziním semestru 2017.
Stránky semináře (archiv): http://www.olsak.net/mirek/manim
Pokud by měl někdo zájem se naučit dělat podobné animace, momentálně bych doporučil se podívat přímo ke zdroji na knihovnu Manim od Granda Sandersona (3Blue1Brown): https://github.com/3b1b/manim
Hudba: Journey's End, autor Vavrek, license CC-BY-SA. https://www.jamendo.com/track/772/journey-s-end
Video ke stažení: http://www.olsak.net/mirek/manim/reklama.mp4
Zdrojový kód: http://www.olsak.net/mirek/manim/reklama.tgz plus EOST fork Manimu: https://github.com/mkoconnor/manim/tree/master/eost
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https://www.youtube.com/watch?v=28MUW4QSY-w
Definition of cardinality comparison, aleph_0 as the least infinite cardinality. Proof that there are aleph_0 many rational numbers but there are uncountable number of infinite binary sequences.
Video download: http://www.olsak.net/mirek/manim/eost/eost02-size-comparison-countable.mp4
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https://www.youtube.com/watch?v=-fMPiNEwsoc
Axiom výběru a dva mírně paradoxní příklady jeho použítí -- nekoneční vězni s klobouky a neměřitelná množina.
Více ke kloboukům: https://www.youtube.com/watch?v=aDOP0XynAzA
Banach Tarski Paradox: https://www.youtube.com/watch?v=s86-Z-CbaHA
Download: http://www.olsak.net/mirek/manim/eost/eost13-AC-cz.mp4
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https://www.youtube.com/watch?v=Bhv81SgqwvM
Kde se ve formálním světě množin vezme kartézský součin
Download: http://www.olsak.net/mirek/manim/eost/eost10b-cartesian-product-formally-cz.mp4
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https://www.youtube.com/watch?v=QcO1jsEEddc
Currest state (as of July, 2019): I have finished the Czech version of the series [1], and I also made an English condensated version without narration [2].
I would like to make an English version once BUT
it is not a priority for me now BUT
if someone would like to contribute to it, I would be pleased to help.
What is necessary to do (and I don't feel confident for it enough, concerning my English level):
1) Check, and possibly fix the current English scripts [3]. It is not only about making it gramatically correct but also making it understandable and natural when narrated (with the animations). The first chapter was seen by more people, so that one should be relatively fine, I think that the others certainly need it before any recording. If you decide to do something with it, please consult your ideas with me (i.e. by XMPP), I have a broader picture of the series, and it is also important to have it compatible with the already created animations. You can notice that the basic English script is for videos in range 1--7. If you make a progress with them, I can provide a basic translation of the following videos.
2) Record a narration. This could be possibly done now for the introduction video.
You can contact me by XMPP: valsorim at jabbim dot cz, or e-mail mirek at olsak dot net.
[1] https://www.youtube.com/playlist?list=PL2m0OzES6Uw-7QDvuWxXnuyHj5BZT40hX
[2] https://www.youtube.com/watch?v=vZhSA7kNOL8
[3] https://github.com/mkoconnor/manim/tree/master/eost
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https://www.youtube.com/watch?v=-8H4jyUDJa8
V naivní teorii množin za určitých okolností vyskakují spory (paradoxy). Kvůli tomu je třeba s množinami zacházet opatrněji, a vybudovat pro ně vlastní formální svět. Jak tenhle svět přesně vypadá si ale ukážeme až příště.
Download: http://www.olsak.net/mirek/manim/eost/eost08-paradoxes-cz.mp4
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https://www.youtube.com/watch?v=DIyar235af8