The (very) basics of sets part one. -- Proof Writing 1

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[abishekpuri]

[20:36] The cartesian product of {1, 2, 3} and {-1, 0, 1} doesn't contain (0, 0), (0, 1) or (0, -1). I think you need to shift all the dots one value to the right :)

[marius]

This is the best series you could make. I absolutely love it. ❤️

[officiallyaninja]

I've been wanting to study proof writing for some time now!
I've been trying to learn real analysis and algebra and I feel like my lack of experience writing proofs is really holding me back, and I'm an engineering major learning math in my free time so it's not like I have a math prof to help me.

[Debg]

Back when I was taking calculus in my first year of uni, we had a not so good professor who expected us to write proofs without any previous teaching on the subject. This would have come in very useful, thank you.

[mitchellyolevsky]

Hi Professor Penn, I've recently started studying math privately as an age 40 something adult with the aid of an awesome individual who is a doctorate candidate and T.A. at the University of Toronto Department of Mathematics. We're currently working through a book called A Readable Introduction To Real Mathematics by Daniel, David and Peter Rosenthal. The content you put out is tremendously helpful as a supplement to the book we're working through. I'm not a very skilled proof writer, but I wanted to thank you for sharing helpful material that benefits people like me who aspire to become more skilled at the craft of mathematical proof writing.

[maldi_tof]

I don't know why I am so excited to see this. 🥰

[onionbroisbestwaifu]

I am taking my first proof writings course next semester, so this was excellently timed!

[ikhu]

14:30 implying pie is a vegetable. jokes aside this is a really good video

[ranakmadan]

omg im so glad i subscribed i am literally learning how to structure number theoretical proofs

[klevisimeri]

I just find motivation every time I watch your videos.

[dylonlarue]

Outstanding book, I’m glad you have a series for it!

[Nys]

The book of Proof is a really nice book, I'm enjoying the idea of this series. Thank you very much for the work, I'll watch it all!

[BethKjos]

Minor disputation: There is no computable upper bound on the number of words in English. There are finitely many words attested on paper at any given moment in history, but it is undecidable whether the language overall admits a finite vocabulary of words which, if pressed, could be made to serve the English tongue.

[pfever]

Amazing course! and unique material on youtube! I really appreciate this! I am an engineer working with artificial intelligence and to advance in research I believe I need to understand mathematics at a deeper level and I think this course will allow me to do that, thank you!

[Nikolas_Davis]

Great, a new series! 😀

btw, the "vegetables in your fridge" set is not well defined if you happen to have tomatoes in your fridge ;-)

[sillymel]

(14:53) Pie isn't a vegetable, Michael.
(16:50) The x-axis is a *subset* of that set, not a member. Also, you haven't defined subset yet.
(20:32) That's {0, 1, 2} × {-1, 0, 1}, not {1, 2, 3} × {-1, 0, 1}.

[Minor_meng]

wow thanks you so much, it's definitely a very useful video

[moshecallen]

Well done but I would have noted that cardinality generally denotes the number of distinct elements. I can write a set which is a countably infinite set of 5's, but by the definition of cardinality that I know of, that would be a set of cardinality 1 until and unless I introduce some manner of distinguishing the elements such as the set of all algebraically defined ways of representing the number 5.

[HarshilHandoo-cmgk]

This is like my discrete structure course but just with the proofs part

[khayalaliyev]

5 and 🥦; Professor, You are a different level of mathematician, a math lover from Azerbaijan 🇦🇿;if mathematics were a game, you would be the one of the final bosses