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Cake day: June 12th, 2023

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  • Kogasa@programming.devtoMemes@lemmy.mlMath
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    19 days ago

    Stokes’ theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f’(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes’ theorem as written says that f(x) - f(a) = integral from a to x of f’(t) dt.











  • Kogasa@programming.devtoMemes@lemmy.ml6÷2(1+2)
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    4 months ago

    The distributive law has nothing to do with brackets.

    The distributive law can be written in PEMDAS as a(b+c) = ab + ac, or PEASMD as ab+c = (ab)+(ac). It has no relation to the notation in which it is expressed, and brackets are purely notational.








  • Kogasa@programming.devtoMemes@lemmy.ml6÷2(1+2)
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    7 months ago

    And that simple model, well-defined model didn’t properly account for juxtaposition, which is how different fields have ended up with two different ways of interpreting it, i.e. strong vs. weak juxtaposition.

    No, that’s just not what happened. “Strong juxtaposition,” while well-defined, is a post-hoc rationalization. Meaning in particular that people who believe that this expression is best interpreted with “strong juxtaposition” don’t really believe in “strong juxtaposition” as a rule. What they really believe is that communication is subtle and context dependent, and the traditional order of operations is not comprehensive enough to describe how people really communicate. And that’s correct.

    Considering your degree specialisation is in solving arithmetic problems

    My degree specialization is in algebraic topology.

    I don’t see the issue with them asking you to put your money where your mouth is and spit out a number if it’s so easy

    The issue is that this question disregards and undermines my point and asks me to pick a side, arbitrarily, that (as I’ve already explained) I don’t actually believe in.

    Ironic that you tell me to check my reading comprehension right after you misquote me, but nonetheless that is the impression your responses have given off - and you haven’t done anything so far to dispel that impression.

    I didn’t misread, you’re in denial.

    Yes, and the question everyone is asking you is what is that unambiguous way? Which side of weak or strong juxtaposition do you come out on?

    Hopefully by this point in the comment you understand that I don’t believe the question makes sense.

    The value judgement was actually more to do with your choice of example, and how you applied that example to this debate. It gave me the distinct impression that you view this debate as not worth having, as anybody who does juxtaposition differently from you is wrong out the gate - and again, your further responses only reinforce my impression of you.

    Again, that’s your fault-- you’ve clearly misinterpreted what I said. If I didn’t think this conversation was worth having I wouldn’t be responding to you.


  • Kogasa@programming.devtoMemes@lemmy.ml6÷2(1+2)
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    7 months ago

    “Which ruleset do you consider correct” presupposes, as the comment said, that there are 2 rulesets. There aren’t. There’s the standard, well known, and simplified model which is taught to kids, and there’s the real world, where adults communicate by using context and shared understanding. Picking a side here makes no sense.


  • Kogasa@programming.devtoMemes@lemmy.ml6÷2(1+2)
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    7 months ago

    Hi, expert here, calculators have nothing to do with it. There’s an agreed upon “Order of Operations” that we teach to kids, and there’s a mutual agreement that it’s only approximately correct. Calculators have to pick an explicit parsing algorithm, humans don’t have to and so they don’t. I don’t look to a dictionary to tell me what I mean when I speak to another human.