Comments by "" (@lamAnyone) on "This Is the Calculus They Won't Teach You" video.

I stopped watching at 6:15. You simply cannot use something flawed to prove itself to be flawless. If something is not smaller and not bigger than must be equal to.....blah blah blah. WHAT? In similar sense, may I say: I am actually my twin brother, or since ∞ and negative ∞ have the same amount of numbers between them and zero, then ∞ must be equal to any other integers and numbers because they have exactly the same relationship with zero?? Mathematics and logic sometimes do not mix, and calculus is built on A LOT OF these mixes. From there, science end up stuck in unexplainable things like dark matter and dark energy. The list goes on and on.
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@jatsko3113 What age did proof by contradiction come from? Yes, from the era that if you could disprove someone being a man, then they must be a woman. I don't think I need to look up the meaning of P.B.C. but I did anyway, for sake of science. Guess what, try googling it and Wikipedia for sure would pop up as the top result. You really should read the last sentence of the first paragraph in that article. I am sorry that I crumbled your perfect true or false binary world, but I am one of those think-out-of-the-box kind of persons. It's about time that people should explore the non-binary options of everything. Not just gender. If Einstein could break the universality of Newton's Laws of Motion, it's just a matter of time that Newton‘s other great invention - calculus got broken.
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@azraellie As I said, sometimes logic and mathematics do not mix. You have to put a lot of scrutiny in this if you consider it's serious mathematics that the great Sir Newton claimed to have invented (he's a laughable figure to me - how many things he claimed to be universal were later proved wrong? That includes his ego.). The <,=,> problem seems like simple logics, yet taking this assumption can have serious consequences to our reality when we casually apply it in real life. We better prove it mathematically, without calculus (did someone used a thousand pages to prove 1+1=2?). I did say we cannot use something flawed to prove something to be flawless. Look up Staircase Paradox. Cutting things into tiny tiny pieces sometimes cannot solve a problem. That's a good example of mathematics conflicting logic. Cutting things up may solve a tailor's problem, but not a vigorous scientist's problem. By the way, I did not say ∞ equals to negative ∞. I am well aware of the vector. I said ∞ would be equal to any number on the same side of the number line relative to zero, e.g. ∞ might equal to 7, negative ∞ might equal to -8 if that set of logics were applied. Of course I know it cannot be.
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@jatsko3113 So if I put 3 persons A, B and C in a dark room. All of a sudden the light turned on. If A and C did not switch the light on, are you 100% sure B is the one switching on the light?
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@jatsko3113 Three options are what we can observe within the lighted dark room, my friend. Sorry, that sounds more like physics. I believe no current mathematician would say our mathematics is complete. We sometimes need to think outside the box, otherwise we are forever stuck with some paradoxes. Calculus has been used for centuries by a lot of brilliant minds ever existed, yet that does not make it automatically impeccable. I think it's flawed, like many other Sir Newton's "inventions" as time goes by. For example, if I have a right-angled triangle with sides 3, 4 and 5 units of length in the Staircase Paradox, an Integral Calculus believer, using their same set of logic, can never explain why the length of the hypotenuse, by calculation, does not gradually collapse from 7 to 5 logarithmically as the slices (or steps) are cut smaller and smaller with rough edges look more and more like a straight line. It stays basically as 3+4, arithmetically and logically. 7 would either logarithmically or mysteriously and suddenly drop to 5 at an undefined spot of the graph if we plot the calculated length of the hypotenuse against number of steps cut, depending on what one believes. Of course, one can also believe that Pythagoras has been wrong all along for millennia and 5 has never been the right answer. The graph stays straight with y=7. That would have prevented the "sudden drop crisis". Should I believe the centuries-old calculus, simple addition and logic, or the millenIa-old Pythagoras' Theorem? That's how I approach a problem. We should always keep our minds open. There are many other symbols on your keyboard, not just <, = and >.
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@jatsko3113 I appreciate your response and your insistence on knowledge you acquired. I maybe a bit not so ordinary, looking from outside the box and I could be wrong too. I am not sure if you are an accomplished mathematician or not. As compared with a, say, physicist, I think a mathematician would be more comfortable with their strict logic behind all those calculations and deductions than all other things, since there are far less real world experiments, observations could be made to prove or disprove their mathematical theories. In physics, they see more and more "laws" broken as technology catches up (think JWST, double slit experiment, etc) When a law is broken, they have to look outside the box for answers. In response to your second paragraph, you didn't seem to be an adamant defender of the pizza example of calculus 4:54 as much as you were. That part of the video said the total area of the curvey edges will approach 0 as slices were cut smaller and smaller - the concept of infinity? Similarly these staircase triangles should have total area approaching zero too - if your frame of reference stays stationary and macroscopic. Yet the idea of those rough staircase edges should never go away - if you move your frame of reference more and more microscopically accordingly, like staring into the screen pixels. I'm not sure how often mathematicians change their frame of reference to get more perspectives of a problem. You tend to agree the roughness never goes away, but you believe 5 is the correct length of the hypotenuse, not 7🤔. To a lot of people, Staircase Paradox is still pretty much a paradox. You just kind of flawlessly illustrated that. I'm not sure about the next paragraph. As we stretch the side of 4 units "infinitely" long, its length will approach that of the hypotenuse, yet the side of 3 units is still there. Theoretically, it is still a triangle, a triangle with hypotenuse "roughly" of the same length as the sum of the other 2 sides. See, playing with the concept of infinity in a practical sense, could be dangerous. When things are approaching infinity, rules start to bend. This infinitely long hypotenuse bit by bit bends your rule of hypotenuse must be shorter than the sum of the other two sides. Here's a bad joke for you: how can you take infinity as limit in your calculus while knowing that technically infinity has no limits??? Your last paragraph: I tried to but have a hard time agree with you. If you and me can prove Pythagoras right with a sandbox, 3 sticks and a tape measure, you would be implying that the other 369 proofs of his theorem (according to Google) irrelevant? In academic fields, it doesn't hurt to have more proofs to something well established. In this case, the point is not Pythagorean Theorem but integral calculus that plays with the dangerous infinity. Unfortunately, both have a lot of practical applications. I think as we apply integral calculus to things ever so smaller and bigger, problems will start to show.
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@ilovelanzhounoodles I fully empathize the hardcore believers of Newtonian gravity wompwomping general relativity before they saw the 1919 solar eclipse with their own eyes. While I am waiting for the next Einstein to come up with fundamental flaws of your calculus, I am also waiting for your calculus to solve all the unsolved mathematical conjectures it could solve. I am open to both and not opinionated. Time and time again Newton had been proved wrong. I just can't wait for the next one, for benefits of all mankind.
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