3blue1brownThe Erdos-Rado Theorem
The Erdos-Rado theorem is a theorem about coloring infinite sets and finding monochromatic subsets. After becoming stumped by the proof of this theorem, I created this video to make sure I understood why the theorem is true.
A basic understanding of cardinals and their operations is needed. You also need to be comfortable taking infinite unions of sets.
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3.1
A nice effort to illustrate a nice proof! In the context of reading along (in e.g. a course or a textbook), I can see this being a very helpful resource. However, on its own as a video, I found it hard to understand due to a lot of notation. I also think that the prerequisites undersell a bit what you need....for example when you use transfinite induction. For a YouTube video format I might consider showing the simplest possible example of the theorem holding (e.g. with finite sets). This is along the lines of the example with 6 vertices you showed...more of that kind of illustration would help draw the viewer in!
3.4
The subect you have choosen is interesting, and the result seems also interesting but i didn't get it, i was lost at 1’ after the 6-> (3)2/2 example, it really became abstract to me. I think this result is complex and it would have need more time to develop and keep making link with the simple example. But it's my first time with coloring function so it may be me.
The rest : quality, rythm, slides, is nice and you know your stuff, please keep going on !
3
The narrative is hard to follow for someone new to this area of math. It feels as though I've joined in the middle of a conversation and missed all the critical context.
5.4
It seems like this theorem and the proof are interesting, but I really couldn’t follow it. If you want the video to be more accessible, you should spend more time explaining what all of the symbols you’re using mean, and also giving a bit more idea of how the proof is going to go before just presenting it.
3.9
This one is a little tough for me to judge since I'm not sure I'm your target audience. As someone who only has a very basic understanding of Set Theory, I got lost pretty quickly a few minutes in and was not able to recover. For someone like me, I think the video would have been more helpful if the pace was a bit slower and more examples were given (credit where it's due: I did really appreciate you giving an example in the early part of the video of what the coloring notation meant. I found it helpful, though it was also said and done a little too quick for my taste).
Overall, it seemed a good video for those with more background than myself, though could use some improvements in pacing and examples and lead-up for those with less background.