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Primes

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  • You're mostly right, i misremembered some stuff. My phone keyboard or my client were not capable of adding a small + to the R. With general prime elements I meant prime elements in a ring. But regarding 3.: Not all reducible elements are prime nor vice versa.

  • Primes

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  • It is no new number, though you can add infinitely many ones to the prime factorisation if you want to. In general we don't append 1 to the prime factorisation because it is trivial.

    In commutative Algebra, a unitary commutative ring can have multiple units (in the multiplicative group of the reals only 1 is a unit, x*1=x, in this ring you have several "ones"). There are elemrnts in these rings which we call prime, because their prime factorisation only contains trivial prime factors, but of course all units of said ring are prime factors. Hence it is a bit quirky to define ordinary primes they way you did, it is not about the amount of prime factors, it is about their properties.

    Edit: also important to know: (ℝ,×), the multiplicative goup of the reals, is a commutative, unitary ring, which happens to have only one unit, so our ordinary primes are a special case of the general prime elements.

  • Primes

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  • Commonly primes are defined as natural numbers greater than 1 that have only trivial divisors. Your definition kinda works, but 1 can be infinitely many prime factors since every number has 1^n with n ∈ ℕ as a prime factor. And your definition is kinda misleading when generalising primes.

  • I'm using duolingo and am almost done with the first big section. It is so different compared to germanic and latin languages! But that was one of the reasons to learn it, so kinda expected. I'm also enjoying it, I don't worry so much about reading and writing and focus on speaking and understanding, like a child would do. Reading and writing is the next step and I hope that it comes somewhat naturally this way.

  • Have you installed Wine? I mean not in Lutris, but actual Wine in Pop!_OS. Then you can just double click the setup.exe like you're in windows, install it where you want and then add it to lutris by adding a game manually.

    That's my prefered way of installing any windows program an most of the time it works.

  • Assuming your goal is to gain knowledge about operating systems

    Try arch but without kde, gnome, xfce, lxqt... make your own DE, based on a WM of your choice. That way you'll gain lods of knowledge about how an OS interacts with the user and which applications do what.

    After that, you would have to go for LFS or Tannenbaums Modern Operating Systems

  • I disagree. I could literally put some porn in this very comment. So the fediverse needs a porn barrier, and every file hoster, we can't allow TOR, there is porn, and illegal porn as well. So please show us your id before entering TOR, pls.

    It is an authoritarian move. It is undermining privacy. It is censoring the web.

    It is parents and maybe schools responsabilty to teach kids how to interact with media, that porn exists and is not an actual representation of sex, and to restrict their access to pornography or media in general.

    Furthermore, on planet earth, there are no perfect democracies, and the democratic system of the USA is flawed to a degree where it is at least questionable if your leaders are elected democratically.

  • TL;DR: Tiny differences in input become huge differences in output in a chaotic system

    You're missing a "can" there. Tiny differences in input can become huge differences in output in a chaotic system. (Infinitely) many chaotic systems are structurally stable. For example consider systems that have the Anosov property.

  • There already dumps of all reddit posts, but uploading them to lemmy would be really bad. Tons of karma farmer bs, countless repost of the 100 most prolific memes, so much porn... and i haven't even started with the massive burden that would hit the federation, hundreds of Terrabytes that need to be stored sonewhere...