Comments by "Brad Camroux" (@camrouxbg) on "Math's Fundamental Flaw" video.

@Kirmeins Yeah, thing is that DM is so vast that it is really easy to set up a course that doesn't touch on any of this material. The DM course I took was like this... introduction to game theory, a little combinatorics and cryptography, coin weighing problems, stuff like that. But I think the important thing is the ability to get students interested in the material, and then they go looking for other courses that cover it.
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@Kirmeins even if you're only studying mathematics, you won't really hear Gödel's name until final year of undergraduate study at the earliest, unless you do an awful lot of advanced reading. Hilbert, on the other hand, has his name scattered throughout undergraduate and graduate topics in mathematics and physics. Gödel's work is considered fairly esoteric and difficult, while Hilbert is more spread out. So it's not surprising that you wouldn't have heard of Gödel if you haven't touched on foundations of maths.
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Why the scare quotes on _bigger_? It is fairly easy to show that the set of real numbers is in fact larger than the set of integers. In fact he did just that in this video.
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@shoam2103 Definitely. Mathematical foundations are not for the faint of heart, but when presented in this way it can become quite accessible. You don't need to be able to DO the math here in order to appreciate it or even talk about it. I haven't watched very much of this channel, and I'm going to have to remedy that.
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@dennispetrov9628 that is a good question. By adding 1 to one digit of each number, this new number will differ from each of the others in one and only one decimal place. Have another careful watch of that segment. I was at first wondering the same thing, but then got it. He does in fact state just what I wrote here. And because this newly constructed number differs from all others, it is not in the list of real numbers. Therefore the list is incomplete and you cannot in fact create such a list.
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@agushernandezquiroga9064 okay, that makes sense. Thanks 😊
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@dennispetrov9628 absolutely. I agree with you. None of this stuff is easy and it is good to sit with it a while and mull it around. I also don't know nearly as much as some others on here. As for the game of meanings, I totally get your meaning (pun intended). For me, though, I have never taken issue with different sizes of infinity. I do understand where people might get hung up, but in my mind it is not unreasonable to say one infinite set is bigger than another infinite set. Perhaps this means I haven't truly understood what's going on, and that's possible. But I think density of numbers and cardinality (size) are two different concepts in math. Someone else on here can probably comment on that, as I'll have to do some more reading and study to get there.
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This is assuming that "god" even exists...
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@tommyrjensen yeah, sorry. I failed to consider the CS folks. They definitely hear about Gödel first.
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This is a phenomenal video! Thanks so much! I would happily watch another 30 or 60 minutes of you talking about and explaining this stuff. Anyone who says mathematics foundations and philosophy of mathematics are dry and boring just hasn't been exposed to it in the right way.
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