This is tragic. I just learned that this professor, Alfonso Gracia-Saz, passed away due to COVID-19 complications. Rest in peace. You truly helped me in my journey towards mastery of calculus.
Thanks Mat I really needed this cause nowI have online school I couldn't use Khan Academy for sets and notation or any book I had on Algebra because I am taking college algebra
1:41 in and I already understand it better then what the onramps the course for college algebra in high school has taught and mostly because I have to read it online
if you watch khann academy and the organic chemistry tutor you prolly know what I'm about to say..but I'm gonna say it anyways... WHAAATT?? Still searching on youtube for math help? Are the videos from 2016 really helpful?
it doesn't have a symbol, example, a set with a symbol with three dots on the end on the elements, it means that set has a symbol but its elements are infinite,
Im in 7th grade but I'm doing 8th grade math and this video is so helpful because my teacher just quickly goes through the lesson thinking that I would understand him with 5 minuets of talking and 85 min of individual work(I have 90 min of class)
By default, I normally always use the symbol "is a subset of and may be equal" unless there is a reason not to. In this case, we know they are not equal. The statement is still true.
What about the sideways U in a 'is a subset of' symbol with a line under it meaning 'or equal' .... but instead of opening towards the right (as in this video) it opens to the left?! Thanks
@@its_my_gaming3229 If you went back to the early 19th century, you would be right. But nowadays both conventions are used. Some mathematicians prefer one, some prefer the other. I think that algebraists and number theorists tend to prefer to include 0, whereas analysts tend to prefer to exclude 0. But even that is not always true. Look at the second paragraph in the Wikipedia page, for example: en.wikipedia.org/wiki/Natural_number Or, see this discussion among mathematicians on Stack Exchange where people argue for both definitions: math.stackexchange.com/questions/283/is-0-a-natural-number There is no correct answer: we can choose to define it one way or the other. The only thing that matters is this: when you read a book or paper, or when you discuss math with a person, be aware of the convention they use. That is all.
@@its_my_gaming3229 in CS theory courses at uoft we treat 0 as a natural number - many reasons for that, like array indices, induction, length of collections, etc - and it’s especially beneficial when we need to prove algorithms (either runtime or correction). Like whoever’s running the channel said, it’s a convention, nothing more nothing less, and if I were to make a proof public I’ll include in the header smth like “we’re counting 0 as a natural number”
@@ieatpancreas2005 It's also called braces. I am not sure if it is an official thing, but I have parsed many lectures and I have come to the consensus that I most likely is due to the fact that many professors and mathematics use "curly braces" instead of "curly brackets". I know that most commonly the curly brackets are called such in programming, especially in c++, JavaScript, and c.
Going to take this down because I have understood just was having a bad day. I am homeschooled and have to RU-vid things every week day of my life. Surely you can understand that everything piles up in my head and don’t understand every little thing. Being home schooled is a hard thing. Btw sorry for wasting these few seconds of your life but I need to let go sometimes and I’m sorry this time it landed on you
