Formerly u/CanadaPlus101 on Reddit.

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Cake day: June 12th, 2023

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  • Haha, I thought it was a homework question. It would be a pretty good one; it’s not hard to answer, but the a proof touches on a lot of things. I probably would have gone about this differently if I hadn’t thought I was addressing someone who’s actively studying these things. Hopefully you still knew most of the terms I was using.

    And the missing part, because including an exercise is low-key a dick move if you were just curious:

    Any basis vector k can’t be 0 (that would be dumb), so if O(k)=0 it fails idempotence and can’t be in the range. Therefore, all kernel bases are not in the range.

    For the range being a subspace, O(a+b)=O(a)+O(b)=a+b, and you can extend that to any linear combination of range vectors.

    I guess you’d need to include the proof that vector (sub)spaces must have a basis to make it airtight, so we know the kernel has any dimensional at all. But, then it’s just the pigeonhole principle, since you can choose a basis for the whole space made up from bases of the two subspaces.

    Best of luck.




  • CanadaPlus@lemmy.sdf.orgtoAsk Lemmy@lemmy.worldIsn't this racism?
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    19 hours ago

    I mean, political apathy is pretty standard in any culture, and there’s no some doubt people - particularly women - enjoyed the wonders of progress and democracy, but there’s always been support for the Taliban as well. That’s how insurgencies work.

    I wasn’t there, but it was mostly fought from within convoys and fortifications, and even when there’s contact you don’t usually tell the guys with guns if you think they’re crazy. Are you sure your sample of local opinion was representative?


  • Definitely.

    It’s a violent world. If you think you can magically opt out of that, somehow, you might have lived a massively privileged life (to this point).

    That being said, look at all the people in the thread who are afraid to admit possible abstract, hypothetical support for something. On a hard-left instance, of an alt platform, that I’m currently using over Tor. That should be an indicator of how much actual will there is to brave a shooting war. (You didn’t ask if we wanna revolution specifically, but this is .ml so I have to address it)

    The practical takeaway of the literal question is much more nuanced and subtle.






  • I would go seriously digging for the source for you, since a cursory search is full of modern stuff and I can’t remember where I saw it exactly, but that would require non-glued fingers.

    If you look at old (siege) engineering manuscripts, they’re full of “take the square root of the armslengths and rewrite as dactyls”-type rules for everything. They didn’t know much about mechanics, and often had funny ideas like momentum being self-dissipating if not sustained. but enough experimentation and basic calculating tools allows you to make rules of thumb anyway.

    And, it’s not like nobody could see how things moved through the air when launched or dropped. Basic principles about falling things go back to the 14th century at least, and the ancient Greeks thought so much about parabolas one must have at least noticed that’s the trajectory of a thrown javelin, albeit without even algebra to start to explain why.

    For example, we don’t need to know about ballistics to use a gun.

    Sure, but you need to know about the trigger and where the bullet comes out of. And, if you don’t know about the recoil, how to load it and where the casing is ejected you might not use it well.

    Thinking about places like Europe and China, there’s probably over a billion people that have never seen a gun operated in real life, so I suppose that’s actually not really necessary, either. On the other hand, I have trouble imagining a modern person who’s never needed to convey “perpendicular”.

    You can define knowledge as enablement to do things.