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Cake day: June 12th, 2023

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  • Kogasa@programming.devtoMemes@lemmy.mlasdf
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    4 months ago

    It doesn’t, it just delegates the responsibility to something else, namely xdg-desktop-portal and/or your compositor. The main issue with global hotkeys is that applications can’t usually set them, e.g. Discord push-to-talk, rather the compositor has to set them and the application needs to communicate with the compositor. This is fundamentally different from how it worked with X11 so naturally adoption is slow.




  • None of the answers are correct. If the answer were 25%, then it couldn’t be 25% because there’s a 50% chance of picking it at random, which contradicts our supposition. Similarly the answer cannot be 50% because there’s a 25% chance of picking it. The answer isn’t 60% because there isn’t a 60% chance of picking it.




  • Kogasa@programming.devtoMemes@lemmy.mlMath
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    5 months 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.devto196@lemmy.blahaj.zoneRule
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    5 months ago

    Going to almost certainly be less than 1. Moving further up the food chain results in energy losses. Those fish are going to use energy for their own body and such

    For sure, which is why I said “another food source would be needed.” I had in mind something like the wild-caught fish being processed into something useful as part of a more efficient food chain, e.g. combined with efficiently-farmed plant material.

    Moreover there’s high mortality rates inside of fish farms for fish themselves.

    I don’t have any context on the other pros and cons of fish farming, so definitely not arguing whether they’re a net positive or not.








  • Kogasa@programming.devto196@lemmy.blahaj.zoneSpectrum rule
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    6 months ago

    “Measure” is meant in the specific sense of measure theory. The prototypical example is the Lebesgue measure, which generalizes the intuitive definition of length, area, volume, etc. to N-dimensional space.

    As a pseudo definition, we may assume:

    1. The measure of a rectangle is its length times its width.

    2. The measure of the disjoint union of two sets is the sum of their measures.

    In 2), we can relax the assumption that the two sets are disjoint slightly, as long as the overlap is small (e.g. two rectangles overlapping on an edge). This suggests a definition for the measure of any set: cover it with rectangles and sum their areas. For most sets, the cover will not be exact, i.e. some rectangles will lie partially outside the set, but these inexact covers can always be refined by subdividing the overhanging rectangles. The (Lebesgue) measure of a set is then defined as the greatest lower bound of all possible such approximations by rectangles.

    There are 2 edge cases that quickly arise with this definition. One is the case of zero measure: naturally, a finite set of points has measure zero, since you can cover each point with a rectangle of arbitrarily small area, hence the greatest lower bound is 0. One can cover any countably infinite set with rectangles of area epsilon/n^(2) so that the sum can be made arbitrarily small, too. Even less intuitively, an uncountably infinite and topologically dense set of points can have measure 0 too, e.g. the Cantor set.

    The other edge case is the unmeasurable set. Above, I mentioned a subdivision process and defined the measure as the limit of that process. I took for granted that the limit exists. Indeed, it is hard to imagine otherwise, and that is precisely because under reasonably intuitive axioms (ZF + dependent choice) it is consistent to assume the limit always exists. If you take the full axiom of choice, you may “construct” a counterexample, e.g. the Vitali set. The necessity of the axiom of choice in defining this set ensures that it is difficult to gain any geometric intuition about it. Suffice it to say that the set is both too “substantial” to have measure 0, yet too “fragmented” to have any positive measure, and is therefore not well behaved enough to have a measure at all.