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#proof

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Marlon Joseph Tesoro Battad

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!?
MWAHAHAHAHAHAHAHAH!!!
youtu.be/5hxgi8hnRBk

YouTubeBLANKNIGHT "OPEN" PRACTICE SESSION FOOTAGE 2022 AND COPYRIGHT ANNOUNCEMENT 2025By Marlon Joseph Tesoro Battad
#MARLONBATTAD#SANCTUS#BLANKNIGHT
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Markus Redeker

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.

I have done that a few times. It is a nice way to organize one's thoughts.

#Proof#Mathematics
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N-gated Hacker News

🎭 Ah, behold the mighty #Anubis, the self-proclaimed savior of #HTTP requests! 🌐 Apparently, it uses #proof-of-work to filter out #AI bots—because who needs efficient solutions when you can just put them to work like #digital 🐴? Just don't mind the placeholder text, it's only there because the developer is battling unforeseen #fame while armed with #React and a dream. 🚀
anubis.techaro.lol/ #bots #development #HackerNews #ngated

anubis.techaro.lolMaking sure you're not a bot!
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Rowan Brad Quni

The sets of all math (M), communication (C), and physical matter (P) are subsets of information (I):

M ⊆ I (M is a subset of I)
C ⊆ I (C is a subset of I)
P ⊆ I (P is a subset of I)

Alternatively, we can express this as the union of the sets:
(M ∪ C ∪ P) ⊆ I (The union of M, C, and P is a subset of I)

#InformationalUniverse #IUH #InformationTheory #Epistemology #DataScience
#Mathematics #Proof #Physics #SetTheory #Ontology #Reality #DigitalAge #AI #QuantumInformation #QNFO #StickyNote

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Akshar Varma

@BernhardWerner My favorite alternative #proof strategy for #induction proofs are #combinatorial (counting) proofs.

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.

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.

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.

Benjamin and Quinn's book on combinatorial proofs is amazing for interpretations of this form (I learned the first proof from it). See also: en.wikipedia.org/wiki/Combinat

en.wikipedia.orgCombinatorial proof - Wikipedia
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WordofTheHour

#proof : that degree of evidence which convinces the mind of any truth or fact, and produces belief

- French: une preuve

- German: abdichten, der Nachweis

- Italian: prova

- Portuguese: prova

- Spanish: prueba

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Fill in missing translations @ wordofthehour.org/r/translatio

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