Welcome to Brain Gainz! My name is Anthony Tucci, and I created this channel to share my passion for mathematics with the world! My goal is to help people better understand math. The videos on this channel will include explanations and example problems in various topics. I am currently working on an algebra series, and once that is done I will move on to trigonometry, then calculus. The different topics will be organised in playlists. Thank you for visiting my channel and thank you for your support!
Hello sir! May I ask if proof by cases is the same as the choose method? I’m confused about the two. The same goes for the Construction method and direct proofs. Are those two the same as well? Please enlighten me. Thanks.
To finish the proof you just have to observe that the epsilon>0 is ARBITRARY: If the absolute disfference of two numbers is less than an ARBITRARY epsilon>0, then the two numbers must necessarily be equal.
Thank you. I have watched 6 videos on this topic, and this is the first one that explained these concepts in a way I could understand. Much appreciated!
That’s not the TI inspire, and no, you would not be satisfied with a five dollar calculator. You obviously don’t know much about math otherwise you would know the difference.
At Q 6.b i'm just confused at the period being 2pi/3 but you drew half of it, shouldn't there be a part of the graph going under the midline as well? Everything else was very helpful thanks!
This is a really positive video, I too am a mathematics student, and recently I've been hit with the pretty common thought in society that studying maths isn't really useful...("should just be an engineer or computer scientist, etc,...".) Seeing you talk about doing what makes you happy and how important that is really hit home to me. Studying mathematics is the future that I want, and it's a future that I see myself being the happiest in. Yes, it is true that we will probably not be the richest, but being rich is truly defined as being happy and proud of the life that you're living. Thank you, Brain Gainz.
I was wondering if this is another valid way to write the proof: Prove the transitive property: If a|b and b|c, then a|c for all positive integers a,b,c. Let’s analyze our first given. We know that a|b. What does it mean for a to divide b? Let l be any positive integer. lℤ+. This means that a times some integer l equals b. Algebraically, we can say: al=b Manipulating this expression to solve for a, we find that: a=b/l Let’s analyze our second given: We know that b|c. What does it mean for b to divide c? Let m be any positive integer. mℤ+. This means that b times some integer m equals c. Algebraically, we can say: bm=c What are we trying to prove? We are trying to prove that a|c. What does it mean for a to divide c? Let n be any positive integer. nℤ+. This means that a times some integer n equals c. Algebraically, we can say: an=c We are trying to prove that a|c. We are trying to prove that an=c where n is some integer. This means we are trying to demonstrate that n=c/a is an integer. We have n=c/a. Recall that c=bm and a=b/l. Let’s replace c with bm. Let’s replace a with (b/l). n=(bm)/(b/l) We multiply bm by the reciprocal of (b/l). n=bm*(l/b) The bs here cancel, leaving us with: n=ml Recall that m is a positive integer. Recall that l is a positive integer. Positive integers are closed under multiplication. This means that the product of two positive integers yields a positive integer. Thus, n must be a positive integer. Since we have confirmed that n is a positive integer, we have confirm that a indeed divides c. Can you let me know whether or not this proof is valid? Thank you :)
How can you solve this this wuestions:Define a relation on R square\(0,0) by letting (x1,y1)equivalence (x2,y2)if there exists a nonzero real number m such that (mx2,my2).prove that relation defines an eqivalence relation on R square \(0,0).What are the corresponding eqivalence classes ?This equivalence relation defines the projective line,denoted by P(R), which is very important in geometry.
great video! Your introduction is really clear and insightful. A lot of times in math, we're just thrown problems and are expected to know the set-up every time with no context. This is where the beauty of math comes. My only contribution to the video would be to show how vertex form would look like...etc. as that is becoming a standard in school, but I honestly follow this method so much better. I think you mentioned that this was a geometric approach, so maybe I'm being too algebraic in my thinking. Thanks for the really great videos. I enjoy your complex polar-coordinate video as well, and it is a new concept for me that I am really intrigued by.
