Comment on I just cited myself.

• ColeSloth@discuss.tchncs.de ⁨4⁩ ⁨days⁩ ago

  I’d just say that not all fractions can be broken down into a proper decimal for a whole number, just like pie never actually ends. We just stop and say it’s close enough to not be important. Need to know about a circle on your whiteboard? 3.14 is accurate enough. Need the entire observable universe measured to within a single atoms worth of accuracy? It only takes 39 digits after the 3.

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  • rockerface@lemm.ee ⁨4⁩ ⁨days⁩ ago

    pi isn’t even a fraction. like, it’s actually an important thing that it isn’t

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    • I_am_10_squirrels@beehaw.org ⁨4⁩ ⁨days⁩ ago

      pi=c/d

      it’s a fraction, just not with integers, so it’s not rational, so it’s not a fraction.

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  • Wandering_Uncertainty@lemmy.world ⁨4⁩ ⁨days⁩ ago

    The problem is, that’s exactly what the … is for. It is a little weird to our heads, granted, but it does allow the conversion. 0.33 is not the same thing as 0.333… The first is close to one third. The second one is one third. It’s how we express things as a decimal that don’t cleanly map to base ten. It may look funky, but it works.

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  • force@lemmy.world ⁨4⁩ ⁨days⁩ ago

    Pi isn’t a fraction – it’s an irrational number, i.e. a number with no fractional form in integer bases. Furthermore, it’s a transendental number, meaning it’s never a solution to f(x) = 0, where f(x) is a non-zero finite-degree polynomial expression with rational coefficients. That’s like, literally part of the definition. They cannot be compared to rational numbers like integer ratios/fractions.

    Since |r|<1 => ∑[n=1, ∞] arⁿ = ar/(1-r), and 0.999… is that sum with a = 9 and r = 1/10 (visually, 0.999… = 9(0.1) + 9(0.01) + 9(0.001) + …), it’s easy to see after plugging in, 0.999… = 9(1/10) / (1 - 1/10) = 0.9/0.9 = 1). This was a proof in Euler’s Elements of Algebra.

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  • sp3tr4l@lemmy.zip ⁨3⁩ ⁨days⁩ ago

    There are a lot of concepts in mathematics which do not have good real world analogues.

    i, the _imaginary number_for figuring out roots, as one example.

    I am fairly certain you cannot actually do the mathematics to predict or approximate the size of an atom or subatomic particle without using complex algebra involving i.

    It’s been a while since I watched the entire series Leonard Susskind has up on youtube explaining the basics of the actual math for quantum mechanics, but yeah I am fairly sure it involves complex numbers.

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    • myslsl@lemmy.world ⁨23⁩ ⁨hours⁩ ago

      i has nice real world analogues in the form of rotations by pi/2 about the origin.

      Since i=exp(ipi/2), if you take any complex number z and write it in polar form z=rexp(it), then multiplication by i yields a rotation of z by pi/2 about the origin because zi=rexp(it)exp(ipi/2)=rexp(i(t+pi/2)) by using rules of exponents for complex numbers.

      More generally since any pair of complex numbers z, w can be written in polar form z=rexp(it), w=uexp(iv) we have wz=(ru)exp(i(t+v)). This shows multiplication of a complex number z by any other complex number w can be though of in terms of rotating z by the angle that w makes with the x axis (i.e. the angle v) and then scaling the resulting number by the magnitude of w (i.e. the number u)

      Alternatively you can get similar conclusions by demoivre’s theorem if you do not like complex exponentials.

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  • ccunning@lemmy.world ⁨4⁩ ⁨days⁩ ago

    pie never actually ends

    I want to go to there.

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• DeanFogg@lemm.ee ⁨4⁩ ⁨days⁩ ago

  Cut a banana into thirds and you lose material from cutting it hence .9999

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  • wholookshere@lemmy.blahaj.zone ⁨2⁩ ⁨days⁩ ago

    That’s not how fractions and math work though.

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• SkyezOpen@lemmy.world ⁨4⁩ ⁨days⁩ ago

  Oh shit, don’t think I saw that before. That makes it intuitive as hell.

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