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#proof
2 posts · 2 participants · 0 posts today
Jan :rust: :ferris:<p>Iris Project | A Higher-Order Concurrent Separation Logic Framework,<br>implemented and verified in the Rocq Prover</p><p><a href="https://iris-project.org/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">iris-project.org/</span><span class="invisible"></span></a></p><p><a href="https://floss.social/tags/FormalVerification" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FormalVerification</span></a> <a href="https://floss.social/tags/Iris" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Iris</span></a> <a href="https://floss.social/tags/ConcurrentSeparationLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ConcurrentSeparationLogic</span></a> <a href="https://floss.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Proof</span></a></p>
Marlon Joseph Tesoro Battad<p>I HEREBY SHEW PROOF THAT I CAN PLAY "EASY MUSIC" AND SING N'AT, AND SIMULTANEOUSLY ANNOUNCE, NAY, DEMONSTRATE WHAT I'VE BEEN DOING TO THIS HYMN FOR, HEH, QUITE SOME TIME NOW! WHO KNOWS HOW LONG ITLL TAKE TO FINE TUNE!? TEN YEARS!? ELEVEN!?<br>MWAHAHAHAHAHAHAHAH!!!<br><a href="https://youtu.be/5hxgi8hnRBk" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">youtu.be/5hxgi8hnRBk</span><span class="invisible"></span></a></p><p><a href="https://mastodon.art/tags/MARLONBATTAD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MARLONBATTAD</span></a> <a href="https://mastodon.art/tags/SANCTUS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SANCTUS</span></a> <a href="https://mastodon.art/tags/BLANKNIGHT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>BLANKNIGHT</span></a> <a href="https://mastodon.art/tags/MARLONJOSEPHTESOROBATTAD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MARLONJOSEPHTESOROBATTAD</span></a> <a href="https://mastodon.art/tags/COPYRIGHT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>COPYRIGHT</span></a> <a href="https://mastodon.art/tags/EASYMUSIC" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>EASYMUSIC</span></a> <a href="https://mastodon.art/tags/PRACTICESESSION" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PRACTICESESSION</span></a> <a href="https://mastodon.art/tags/PIANO" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PIANO</span></a> <a href="https://mastodon.art/tags/ONEMANBAND" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ONEMANBAND</span></a> <a href="https://mastodon.art/tags/LATINTRANSLATION" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LATINTRANSLATION</span></a> <a href="https://mastodon.art/tags/CHURCHLATINTRANSLATION" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CHURCHLATINTRANSLATION</span></a> <a href="https://mastodon.art/tags/OPENCREATIVEPROCESS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>OPENCREATIVEPROCESS</span></a> <a href="https://mastodon.art/tags/HOSANNA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HOSANNA</span></a> <a href="https://mastodon.art/tags/PROOF" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PROOF</span></a> <a href="https://mastodon.art/tags/WIPWEDNESDAY" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>WIPWEDNESDAY</span></a></p>
Markus Redeker<p>Proof by starvation: This is a proof form in which you first prove that a counterexample to the theorem must have property X, then, using X, prove that it must also have property Y, then that it must also have property Z, ... until you have piled up so many requirements on a counterexample that everybody sees that it cannot exist.</p><p>I have done that a few times. It is a nice way to organize one's thoughts.</p><p><a href="https://mathstodon.xyz/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Proof</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a></p>
Knowledge Zone<p>Is the <a href="https://mstdn.social/tags/Birthday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Birthday</span></a> <a href="https://mstdn.social/tags/Paradox" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Paradox</span></a> real? : Medium</p><p>How to Be More <a href="https://mstdn.social/tags/Assertive" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Assertive</span></a> - Without Being ‘<a href="https://mstdn.social/tags/Rude" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Rude</span></a>’ or ‘<a href="https://mstdn.social/tags/Aggressive" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Aggressive</span></a>’ : Misc</p><p>How <a href="https://mstdn.social/tags/Anime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Anime</span></a> <a href="https://mstdn.social/tags/Fans" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Fans</span></a> <a href="https://mstdn.social/tags/Stumbled" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Stumbled</span></a> upon a <a href="https://mstdn.social/tags/Mathematical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematical</span></a> <a href="https://mstdn.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Proof</span></a> : Sci Am</p><p>Check our latest <a href="https://mstdn.social/tags/KnowledgeLinks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>KnowledgeLinks</span></a></p><p><a href="https://knowledgezone.co.in/resources/bookmarks" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">knowledgezone.co.in/resources/</span><span class="invisible">bookmarks</span></a></p>
Akshar Varma<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@BernhardWerner" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>BernhardWerner</span></a></span> My favorite alternative <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> strategy for <a href="https://mathstodon.xyz/tags/induction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>induction</span></a> proofs are <a href="https://mathstodon.xyz/tags/combinatorial" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>combinatorial</span></a> (counting) proofs.</p><p>I suppose the standard example might be the proof of the coefficients in the binomial theorem expansion, or for the sum of binomial coefficients being powers of 2. These can be proved by induction, of course, but I'm not sure that's common given how easier it is to do a counting proof. It is also much clearer and avoids tedious algebra.</p><p>One I like is proving that the sum 1 + 2 + 3 + ⋯ + 𝑛 is 𝑛 + 1 choose 2, the binomial coefficient \(\binom{n+1}{2}\). Bijection proof, counts the same thing in two ways. The thing being counted is the number of ways of choosing two things (distinct, without repetition) from the set {0, 1, ..., 𝑛}. By definition, it is the binomial coefficient we want. The other way to count is to fix the larger number 𝑘, the remaining choices are any of the 𝑘 numbers from 0 to 𝑘 - 1. Thus, across all possible larger numbers, we get the sum from 1 to n.</p><p>An alternative alternate proof of the same, slightly more geometric is as follows: arrange dots in a triangle, 1 on row 1, 2 on row 2, and so on up to row n, with n dots. Add a phantom row of n+1 dots below. We want to add up all dots in first n rows: ∑ 𝑖. If you think of all of this as a binary tree/DAG, then every dot has two children (imagine Pascal's triangle). If you pick any two dots in the phantom row, their common ancestor is unique. So counting dots is same as picking two dots in phantom row. Which is the binomial coefficient we want.</p><p>Benjamin and Quinn's book on combinatorial proofs is amazing for interpretations of this form (I learned the first proof from it). See also: <a href="https://en.wikipedia.org/wiki/Combinatorial_proof" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Combinat</span><span class="invisible">orial_proof</span></a></p>
WordofTheHour<p><a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> : that degree of evidence which convinces the mind of any truth or fact, and produces belief</p><p>- French: une preuve</p><p>- German: abdichten, der Nachweis</p><p>- Italian: prova</p><p>- Portuguese: prova</p><p>- Spanish: prueba</p><p>------------</p><p>Fill in missing translations @ <a href="https://wordofthehour.org/r/translations" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">wordofthehour.org/r/translatio</span><span class="invisible">ns</span></a></p>
getmisch<p>Flag down on the play, B&H Photo-Video! Was repeatedly assured in-store that buying items & having them shipped would not incur any charges (I bought $200 of stuff!). So when it shipped & I saw a shipping charge, I called right away. Not like them, they're usually more honest.<br><a href="https://masto.nyc/tags/B" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>B</span></a>&H <a href="https://masto.nyc/tags/Photo" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Photo</span></a> <a href="https://masto.nyc/tags/Video" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Video</span></a> <a href="https://masto.nyc/tags/Store" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Store</span></a> <a href="https://masto.nyc/tags/free" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>free</span></a> <a href="https://masto.nyc/tags/shipping" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>shipping</span></a> <a href="https://masto.nyc/tags/not" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>not</span></a> <a href="https://masto.nyc/tags/really" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>really</span></a> <a href="https://masto.nyc/tags/called" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>called</span></a> for <a href="https://masto.nyc/tags/credit" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>credit</span></a> <a href="https://masto.nyc/tags/back" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>back</span></a> <a href="https://masto.nyc/tags/filter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>filter</span></a> <a href="https://masto.nyc/tags/holder" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>holder</span></a> <a href="https://masto.nyc/tags/effects" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>effects</span></a> <a href="https://masto.nyc/tags/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>photography</span></a> <a href="https://masto.nyc/tags/pictures" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>pictures</span></a> <a href="https://masto.nyc/tags/instant" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>instant</span></a> <a href="https://masto.nyc/tags/color" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>color</span></a> <a href="https://masto.nyc/tags/black" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>black</span></a>& <a href="https://masto.nyc/tags/white" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>white</span></a> <a href="https://masto.nyc/tags/negatives" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>negatives</span></a> <a href="https://masto.nyc/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> <a href="https://masto.nyc/tags/sheet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>sheet</span></a> <a href="https://masto.nyc/tags/roll" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>roll</span></a> <a href="https://masto.nyc/tags/film" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>film</span></a> <a href="https://masto.nyc/tags/bellows" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>bellows</span></a> <a href="https://masto.nyc/tags/camera" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>camera</span></a> <a href="https://masto.nyc/tags/shoot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>shoot</span></a></p>
claude<p>inspired by tavis' deep field <a href="https://post.lurk.org/tags/nebulabrot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>nebulabrot</span></a> <a href="https://post.lurk.org/tags/DeepZoom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DeepZoom</span></a> images on <a href="https://post.lurk.org/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fractal</span></a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fractals</span></a> forums, I did a little shader that for each c in the complement of the <a href="https://post.lurk.org/tags/MandelbrotSet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MandelbrotSet</span></a> M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).</p><p>it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.</p><p><a href="https://post.lurk.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a> <a href="https://post.lurk.org/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> <a href="https://post.lurk.org/tags/ComplexDynamics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ComplexDynamics</span></a></p>
Jan :rust: :ferris:<p>‘Interpretability’ and ‘alignment’ are fool’s errands: a <a href="https://floss.social/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> that controlling misaligned large language models is the best anyone can hope for (Oct 2024)</p><p><a href="https://link.springer.com/epdf/10.1007/s00146-024-02113-9?sharing_token=3rRsMdH1UdNlnQQmqcozX_e4RwlQNchNByi7wbcMAY6BPcdnFvH2qz5wBW_MWVfuP6XiIjUuOaAkAylpJWYcV7ptG9FICiiQIbLIhD2SwblgAxawIQPIF0AJKzQaIv6wgiJRo4GtMJ1R6AewBvbdRekNszwAag_WVijImJA2dlc%3D" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">link.springer.com/epdf/10.1007</span><span class="invisible">/s00146-024-02113-9?sharing_token=3rRsMdH1UdNlnQQmqcozX_e4RwlQNchNByi7wbcMAY6BPcdnFvH2qz5wBW_MWVfuP6XiIjUuOaAkAylpJWYcV7ptG9FICiiQIbLIhD2SwblgAxawIQPIF0AJKzQaIv6wgiJRo4GtMJ1R6AewBvbdRekNszwAag_WVijImJA2dlc%3D</span></a></p><p>"This paper [...] show[s] that it is empirically impossible to reliably interpret which functions a large language model (<a href="https://floss.social/tags/LLM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LLM</span></a>) <a href="https://floss.social/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AI</span></a> has learned, and thus, that reliably aligning LLM behavior with human values is provably impossible."</p><p>This affects much more than just alignment!</p><p><a href="https://floss.social/tags/LLMs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LLMs</span></a> <a href="https://floss.social/tags/Paper" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Paper</span></a> <a href="https://floss.social/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ArtificialIntelligence</span></a></p>
Knowledge Zone<p><a href="https://mstdn.social/tags/Proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Proof</span></a> of <a href="https://mstdn.social/tags/Perfection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Perfection</span></a> : Medium</p><p><a href="https://mstdn.social/tags/Scientists" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Scientists</span></a> figured out the <a href="https://mstdn.social/tags/Optimal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Optimal</span></a> cup of <a href="https://mstdn.social/tags/Coffee" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Coffee</span></a> : Pop Sci</p><p><a href="https://mstdn.social/tags/Physicists" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physicists</span></a> describe <a href="https://mstdn.social/tags/Exotic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Exotic</span></a> ‘<a href="https://mstdn.social/tags/Paraparticles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Paraparticles</span></a>’ that defy <a href="https://mstdn.social/tags/Categorization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Categorization</span></a> : Nature</p><p>Check our latest <a href="https://mstdn.social/tags/KnowledgeLinks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>KnowledgeLinks</span></a></p><p><a href="https://knowledgezone.co.in/resources/bookmarks" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">knowledgezone.co.in/resources/</span><span class="invisible">bookmarks</span></a></p>
EVSHIFT<p><a href="https://www.evshift.com/317354/since-1975-the-ultimate-proof-that-small-can-also-be-big-our-polo-%f0%9f%9a%97%f0%9f%a4%a9/" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">evshift.com/317354/since-1975-</span><span class="invisible">the-ultimate-proof-that-small-can-also-be-big-our-polo-%f0%9f%9a%97%f0%9f%a4%a9/</span></a> Since 1975 the ultimate proof that small can also be big: our Polo 🚗🤩 <a href="https://channels.im/tags/Big" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Big</span></a> <a href="https://channels.im/tags/ElectricCars" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ElectricCars</span></a> <a href="https://channels.im/tags/ElectricVehicles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ElectricVehicles</span></a> <a href="https://channels.im/tags/EV" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>EV</span></a> <a href="https://channels.im/tags/polo" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>polo</span></a> <a href="https://channels.im/tags/PROOF" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PROOF</span></a> <a href="https://channels.im/tags/Small" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Small</span></a> <a href="https://channels.im/tags/ultimate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ultimate</span></a> <a href="https://channels.im/tags/volkswagen" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>volkswagen</span></a></p>
issdeinschnitzelBirds aren't real. <a class="hashtag" href="https://gleasonator.com/tag/proof" rel="nofollow noopener noreferrer" target="_blank">#proof</a><span class=""><br><br>RT: <a href="https://mostr.pub/objects/99896ca31b20d7f504e1cd3a89f59fb282c7b6ecedcc3dee5b3a78d9e3403425" rel="nofollow noopener noreferrer" target="_blank">https://mostr.pub/objects/99896ca31b20d7f504e1cd3a89f59fb282c7b6ecedcc3dee5b3a78d9e3403425</a></span>
getmisch<p>Over seventy percent of the <a href="https://masto.nyc/tags/GOP" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GOP</span></a> wants to see the <a href="https://masto.nyc/tags/white" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>white</span></a> <a href="https://masto.nyc/tags/supremacist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>supremacist</span></a> <a href="https://masto.nyc/tags/terrorists" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>terrorists</span></a> <a href="https://masto.nyc/tags/pardoned" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>pardoned</span></a>, for shitting in the <a href="https://masto.nyc/tags/Capitol" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Capitol</span></a> and spreading it on the walls, for parading a <a href="https://masto.nyc/tags/confederate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>confederate</span></a> <a href="https://masto.nyc/tags/flag" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>flag</span></a> there for the first time, for trying to <a href="https://masto.nyc/tags/kill" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>kill</span></a> the <a href="https://masto.nyc/tags/vice" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>vice</span></a> <a href="https://masto.nyc/tags/president" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>president</span></a> and trying to <a href="https://masto.nyc/tags/overthrow" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>overthrow</span></a> the <a href="https://masto.nyc/tags/government" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>government</span></a> in a <a href="https://masto.nyc/tags/violent" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>violent</span></a> coup. Zero <a href="https://masto.nyc/tags/evidence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>evidence</span></a>, lost over sixty cases, no <a href="https://masto.nyc/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> yet they lie still.<br>They were terrorists, not rioters (<a href="https://masto.nyc/tags/rioters" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>rioters</span></a> have legit grievances).<br><a href="https://masto.nyc/tags/never" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>never</span></a> <a href="https://masto.nyc/tags/forget" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>forget</span></a> <a href="https://masto.nyc/tags/Jan6" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Jan6</span></a> <br><a href="https://www.cbsnews.com/news/poll-analysis-republicans-jan-6-attack/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">cbsnews.com/news/poll-analysis</span><span class="invisible">-republicans-jan-6-attack/</span></a></p>
Akshar Varma<p>For anyone interested, here are links to the relevant sections of Wikipedia pages for the proofs in order:</p><p>1. Well-Ordering Principle<br><a href="https://en.wikipedia.org/wiki/Well-ordering_principle#Properties" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Well-ord</span><span class="invisible">ering_principle#Properties</span></a></p><p>2. Euclidean Division<br><a href="https://en.wikipedia.org/wiki/Euclidean_division#Proof" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Euclidea</span><span class="invisible">n_division#Proof</span></a></p><p>3. Bézout's identity<br><a href="https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity#Existence_proof" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/B%C3%A9z</span><span class="invisible">out%27s_identity#Existence_proof</span></a></p><p>4. Euclid's Lemma<br><a href="https://en.wikipedia.org/wiki/Euclid%27s_lemma#Using_B%C3%A9zout's_identity" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Euclid%2</span><span class="invisible">7s_lemma#Using_B%C3%A9zout's_identity</span></a></p><p>5. Unique Prime Factorization<br><a href="https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Proof" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Fundamen</span><span class="invisible">tal_theorem_of_arithmetic#Proof</span></a></p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>prime</span></a></p>
Akshar Varma<p>For a long time, I didn't know exactly how the Fundamental Theorem of Arithmetic (unique prime factorization) was proved from first principles.</p><p>I finally figured out the order of proofs for the fundamental theorem of arithmetic from first principles. Now that I know the sequence, it feels like it was my own fault for not properly going through a textbook and that it was probably obvious to everyone. I'm posting this mainly to reinforce my own clarity on the topic.</p><p>1. Well-Ordering Principle, this is either taken as axiomatic or one step away from axioms. This is where I'm drawing the line for "first principles".<br>2. Euclidean Division: Existence and Uniqueness of quotient 𝑞 and remainder 𝑟 in 𝑎 = 𝑞𝑏 + 𝑟 form. Uniqueness if 𝑟 between [0,1,...,𝑞−1]. Proof is just well-ordering principle (often framed as infinite descent).<br>3. Bezout's Identity. Proof starts with well-ordering to find 𝑑, then together with Euclidean division shows that 𝑑 is a divisor. A bit more Euclidean division shows that all other factors 𝑑' also divide 𝑑. So 𝑑 is the greatest divisor.<br>4. Euclid's Lemma: Proof says if 𝑝 doesn't 𝑎 in product 𝑎𝑏, then gcd(𝑎,𝑝)=1. This brings in the above and some rearrangement proves that 𝑏 is a factor as needed.<br>5. Fundamental Theorem of Arithmetic: Existence usually goes via strong induction (which can be rephrased as Well-Ordering + contradiction). Uniqueness uses Euclid's Lemma to show that the primes in the factorization must divide each other (which implies equality).</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>prime</span></a></p>
Rafael<p>I'm still working through that algebra and trig book by Fisher and Ziebur. I just finished the section on linear functions and I picked up another gem. I always knew that y=mx+b was linear but I'd never seen it proved. Or even thought about proving it. But, they provide a nice proof (starting on p.64). There isn't space to reproduce it here but it relies on the triangle inequality and is a satisfying bit of algebra!</p><p><a href="https://mastodon.sdf.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mastodon.sdf.org/tags/algebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>algebra</span></a> <a href="https://mastodon.sdf.org/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a></p>
Susan Larson ♀️🏳️🌈🏳️⚧️🌈<p><a href="https://mastodon.online/tags/LGBTQ" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LGBTQ</span></a> groups <a href="https://mastodon.online/tags/voice" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>voice</span></a> ‘grave <a href="https://mastodon.online/tags/concerns" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>concerns</span></a>’ over <a href="https://mastodon.online/tags/policy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>policy</span></a> <a href="https://mastodon.online/tags/prohibiting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>prohibiting</span></a> <a href="https://mastodon.online/tags/ID" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ID</span></a> updates without <a href="https://mastodon.online/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> of <a href="https://mastodon.online/tags/GenderAffirmingSurgery" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GenderAffirmingSurgery</span></a> in <a href="https://mastodon.online/tags/letter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>letter</span></a> to <a href="https://mastodon.online/tags/Missouri" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Missouri</span></a> <a href="https://mastodon.online/tags/DepartmentofRevenue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DepartmentofRevenue</span></a>. </p><p>“Not all <a href="https://mastodon.online/tags/trans" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>trans</span></a> <a href="https://mastodon.online/tags/people" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>people</span></a> choose to undergo <a href="https://mastodon.online/tags/surgery" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>surgery</span></a> as part of their <a href="https://mastodon.online/tags/genderaffirmingcare" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>genderaffirmingcare</span></a>” </p><p><a href="https://mastodon.online/tags/Women" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Women</span></a> <a href="https://mastodon.online/tags/Transgender" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Transgender</span></a> <a href="https://mastodon.online/tags/LGBTQ" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LGBTQ</span></a> <a href="https://mastodon.online/tags/LGBTQIA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LGBTQIA</span></a> <a href="https://mastodon.online/tags/Missouri" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Missouri</span></a> <a href="https://mastodon.online/tags/Conservatives" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Conservatives</span></a> <a href="https://mastodon.online/tags/Extremism" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Extremism</span></a> <a href="https://mastodon.online/tags/Fascism" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Fascism</span></a> <a href="https://mastodon.online/tags/Religion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Religion</span></a> <a href="https://mastodon.online/tags/Hategroups" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Hategroups</span></a> <a href="https://mastodon.online/tags/RepublicanParty" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>RepublicanParty</span></a> <a href="https://mastodon.online/tags/Hate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Hate</span></a> <a href="https://mastodon.online/tags/Bigotry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Bigotry</span></a> <a href="https://mastodon.online/tags/Violence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Violence</span></a> <a href="https://mastodon.online/tags/Genocide" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Genocide</span></a> <a href="https://mastodon.online/tags/Discrimination" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Discrimination</span></a> <a href="https://mastodon.online/tags/Transphobia" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Transphobia</span></a> <a href="https://mastodon.online/tags/ThePartyOfHate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ThePartyOfHate</span></a> <a href="https://mastodon.online/tags/EmptyThePews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>EmptyThePews</span></a> </p><p><a href="https://www.stlpr.org/show/st-louis-on-the-air/2024-12-09/lgbtq-groups-voice-grave-concerns-over-id-change-in-letter-to-missouri-dor" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">stlpr.org/show/st-louis-on-the</span><span class="invisible">-air/2024-12-09/lgbtq-groups-voice-grave-concerns-over-id-change-in-letter-to-missouri-dor</span></a></p>
gellenburg :heart_pride: :verified_gay:<p><a href="https://hostux.social/@fsf" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@fsf@hostux.social</a> I'm going to need to see some <a href="https://queerfedi.com/tags/proof" rel="nofollow noopener noreferrer" target="_blank">#proof</a> and <a href="https://queerfedi.com/tags/evidence" rel="nofollow noopener noreferrer" target="_blank">#evidence</a> of your claim that <a href="https://queerfedi.com/tags/Widevine" rel="nofollow noopener noreferrer" target="_blank">#Widevine</a> provides a hardware <a href="https://queerfedi.com/tags/backdoor" rel="nofollow noopener noreferrer" target="_blank">#backdoor</a> into my machine, considering that it's a <a href="https://queerfedi.com/tags/software" rel="nofollow noopener noreferrer" target="_blank">#software</a><span> component.<br><br>Do you happen to have a source for that claim?<br><br>RE: </span><a href="https://hostux.social/users/fsf/statuses/113608596180249339" rel="nofollow noopener noreferrer" target="_blank">https://hostux.social/users/fsf/statuses/113608596180249339</a></p>
𝚛𝚊𝚝<p>When you look someone up and find they died some years ago; one of my old lecturers:<br><a href="https://blogs.cs.st-andrews.ac.uk/csblog/2018/09/04/dr-roy-dyckhoff/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">blogs.cs.st-andrews.ac.uk/csbl</span><span class="invisible">og/2018/09/04/dr-roy-dyckhoff/</span></a><br><a href="https://social.sdf.org/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://social.sdf.org/tags/compsci" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>compsci</span></a> <a href="https://social.sdf.org/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> <a href="https://social.sdf.org/tags/topology" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>topology</span></a> <a href="https://social.sdf.org/tags/logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>logic</span></a> <a href="https://social.sdf.org/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>proof</span></a> <a href="https://social.sdf.org/tags/belatedrip" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>belatedrip</span></a></p>
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