Comments by "" (@zachrodan7543) on "Another Roof" channel.

  1. Watching that intro was sublime This will be a fun usage of my time
    5
  2. 21:33 that was BY FAR the most convincing argument i have heard for demoting pluto from planethood.
    3
  3. Another way to justify nC0=1 is that nCk could be interpreted as Given a set with n elements, how many subsets are there with k elements. Every set has the empty set as a subset, and since a set is only defined by its elements, there is exactly one empty subset.
    2
  4. Like you, i first concieved of this problem as a child, and also in terms of n=5... although in my formulation it was always just about ways of arranging the numbers while separating consecutive numbets. I then spent all of last summer quarter working out the answers for up to n=8... by creating an adjacency graph, counting the allowable hamiltonian paths and circuits on those graphs, and then using some symmetry to get the final counts (there are as many ways to start at 1 and end at 2 as there are ways to start at n and end at n-1; you can go either direction on a path, and you can start at any point on a path that is a closed loop) Probably doesn't help my attempts that i apparently undercounted, at least in the case od n=6, where I only found 76 ways to do it... [Insert mathematically flavored profanity here]
    2
  5. As a math tutor who frequently is helping people with calculus, i have a very intimate awareness of some of the most egregious examples of math that you learn in school with no real applications: upper and lower reimann sums (in which you go out of your way to do extra work to get as bad an estimate possible while still being constrained to function values), and error approximation methods for any of the various approximation methods learned in calculus (which are less inapplicable, and more outdated relics: they are taught alongside those approximation methods because the approximations themselves are useful, either as quick estimates, or as conceptual building blocks, and the people who worked out these approximation methods didn't have computers to turn to if they wanted better approximations to compare to, so they had to find ways to approximate the error on their calculations) I don't particularly mind that the error estimation methods are taught, since they at least can be helpful in illustrating how good or bad an approximation method is. However, the fact that students learning about reimann sums are being forced to learn about the upper and lower reimann sums alongside the left, right, and midpoint sums, is frankly inexcusable to me: the upper and lower sums are so useless that when i searched google for when they might be used, there was not a single result on the first page which answered the question being asked; and they don't have any interesting properties on their own either, since they are just doing extra work to get a worse estimate. If you are going to make the students do extra work in their integral estimations, at least do simpsons rule over upper ajd lower reimann sums (and please don't do simpsons rule either, as while it at least gives you better precision for not a horrid amount of extra work, it is not enough to justify using simpsons rule, especislly if you then have to deal with the simpsons rule error approximation formula, which i recall being almost as atrocius as the cubic formula...)
    2
  6. If you haven't already made a video about it, another mathematical rivalry which would be interesting to see your breakdown of is the one between newton and liebniz
    1
  7. 34:02 as many of us who have taken a decent amount of calculus classes (at least 2-3, depending on the school you take them out) know, assuming f is infinitely differentiable, it can be written as a polynomial. However, it might have infinite non-zero terms... which still might become problematic if your method depends on finding all the coeficients so that you can then solve for u...
    1
  8. "A really huge number, like 17" 6 be like "am i a joke to you?!" Meanwhile, 17 responds by feeling self-conscious about it's size, after you called it fat, when it thought the "huge" numbers didn't start until 18
    1
  9. 1:18 no. Archimedes was doing integrals long before fermat was even born
    1
  10. 23:00 10^74 being "very big" 17, from your video on addition: "see? How dare you call me huge, when that behemoth only gets called 'big'"
    1
  11. This may be a silly question, posed by someone who is not yet at the level of math education where i have the ability to start studying group theory (i'm working on it: i am taking the prerequisite class to apply for declaring a math major this fall), but given that M24 contains M23, just by fixing an element in place; and M23 contains M22 likewise, and M22 contains a lee group by the same logic (and presumably the pattern continues downwards), how do we know for certain that M24 isn't a subgroup of some other group going the other direction, which could then have more transitivity? Or do we know for certain that this hypothetical "M25" doesn't exist?
    1
  12. If a function must be defined in such a way that every element of the input set has a clear instruction on where to find its pair in the output set, how do we justify calling things like y=1/x a function, when x=0 doesn't map to anything?
    1
  13. 16:41 do you mean to be talking about integers here? Because if we require a unique prime factorization, then allowing for negative prime factors lets us have multiple prime factorizations of the same number (2x3=(-2)x(-3)=6). From what i can tell, the claims you are making here are only true for the natural numbers greater than 1...
    1
  14. "Man has dog hair on trousers Therefore, man likely works at buckingham palace" Has got to be one of the worst inferences i can think of to make from a man having dog hair on their trousers: wouldn't it be more reasonable to assume that a man with dog hair on his trousers has a dog?
    1
  15. 12:36 you should have him lay them face-up, in a mathematically sensible order as you walk up the path...
    1
  16. Not sure why 9 would be considered perfect... 6, on the other hand, does meet the definition of a perfect number: its non-self factors add to itself. A property shared by very few numbers. 28 and 496 are the next two smallest such numbers.
    1
  17. 5:19 the curse of simple math strikes again and claims yet another victim. As a general rule, if something seems too easy to be right in mathematics, try it anyways. Sometimes, math is just that easy, and all the sidequests it sends you down are merely distractions.
    1
  18. 12:19 i tutor students up to calc, and i think i can safely say that being a trained mathematician has nothing to do with a tendency to overcomplicate things... one of my greatest joys in my job is how often i get to respond with "yes" to people incredulously asking "it's that easy?!"
    1
  19. That intro alone earned my subscribe and my like... and i sort of know enough math to know where you are going, so now my biggest hanging question is "cake?" (Also, what route are you taking to the definition of three indicated by the thumbnail, and how does cake factor into said definition)
    1
  20. 3:47 I would only bet my life on it if i had absolute confident that they would not make any mistakes in the calculation. With such large numbers, i would be hesitant to trust someone working by hand to keep it organized enough that they don't make any careless mistakes...
    1
  21. If there is no risk of human error, though, i will bet my life on that always giving the same answer (which i am too lazy to type into a computer to calculate right now)
    1
  22. 9:43 i feel like a more likely way to get around the lack of a perfect match is that perhaps the rooms move differently if there is a room in the space they are trying to occupy. After all, in the row above the row you have circled, the first two rooms are in the same location, and it is probably a safe assumption that any given set of coordinates can only be occupied by one room at a time.
    1
  23. My immediate reaction to any claims of ai being competent at math is "not if the ai is chat gpt". Last week was finals week, and i had multiple students i was tutoring who were getting tripped up by chatgpt doing bad integration...
    1
  24. After seeing your demonstration, i see that my claims about why chatgpt wasn't doing it right were spot-on: unlike the ai in question in this video, chat gpt doesn't have the help of a deduction engine. Or as I like to put it when telling students to not use chatgpt (if you must ask a computer to help you solve a problem, ask wolframalpha, which at least knows what it is doing, even if it isn't always forthcoming on what exactly that process is): "ChatGPT knows very little beyond the likelyhood of what the next character will be in the string of text it is creating"
    1