Another fantastic video! These are amazing, dude. Thank you so much. I have just recently started doing some math (yeah, lockdown has led me to do actual math lol) after not doing it for a long time, and these really hit the spot!
@@RandellHeyman I am only really doing sorta A level (UK) stuff, but did some line-slope, trig, and basic algebra as a warm up. One thing I wondered about, is how to know when to do something and when not. For example, in this video, I paused and was working it out and then combined the denominator, which made things go wrong, as he split it into fractions with each using the denominator: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CDXoOCVi7D0.html (sorry the guy has awful handwriting lol!) How do you know when to combine and when not? And in this one (yeah I watch all sorts lol) he has (k+1)^5 and changes it to (K-1+2) (I still find induction weird lol) and how did he know to do that? Sorry if this seems like a lot to ask!
@@marienbad2 I don't know what you mean by combined the denominators and then some of the things after that. It's better to ask as clearly as possible, for example, how do you add a/b + c/d where b and d are not equal to zero?
@@RandellHeyman Also I forgot to link the other video lol - it was this one: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6O1s3_GsSHo.html so to add the fractions it is (ad+bc)/bd . I think I have linked the wrong video lol. Sorry.
It is easy to visualise 3 or less variables. Can you show us how to do with 4, 5 or even 10. I start to confuse which area should be subtracted and which ones should be added back to compensate. Thanks.
Man la If you search online you can find venn diagrams for 4 and 5 sets. But in practice you need to use set notation (what I call the algebraic method). The inclusion-exclusion principle works fine....just add all the single sets then subtract all the intersections of 2 sets then add all the intersections of 3 sets then subtract all the intersections of 4 sets etc.
I'm thinking back to the Venn triangle - and yeah. Thanks for that good advice. And this vid. However, once you get past 5, it becomes pretty clear you need to use something else - unless you want to be writing things out for too long, of course. And if there isn't, I admit I'll be sad, but oh well.
This video saved me! I am working through Stats with Julia book (people.smp.uq.edu.au/YoniNazarathy/julia-stats/StatisticsWithJulia.pdf). It's a bit above my level. On page 60 of the book there's a formula for the general expression of the inclusion/exclusion principle that nearly made me give up reading the book but this video shifted the concept from "above my head" to relatively trivial. Thank you so much. I need a tutor like you.
Good point. In retrospect I probably should have mentioned that. I think most viewers who have got to the point of working on problems will have been taught that `or' means`inclusive or'. Some will pick up the intended meaning of the word `or' as they try to make sense of problem(s) using this principle. Thanks for the comment.
