"All questions of the Law are to be decided only by appeal to my writings, each for himself."—The (Tunis) Comment https://hermetic.com/legis/tunis/index
As the curatorial and investigative journalist Prof. #SethAbramson showed in his national bestseller on the Russia-Ukraine crisis—#Proof of #Corruption (#Macmillan, 2020)—, there were ample connections between the #Kremlin and #Kyiv during that period; to say the least.
#PROOF! The CHUMP Has ZERO CONTROL OVER STOCK MARKETS. This convicted felon has no more than a Grade 8 Education. He has never paid any CONSEQUENCES in his life!
You have just EXPERIENCED yet another #FLASH_CRASH MANY MORE TO COME!
#NEWSFLASH! The Securities & Exchange Commission & the Commodities Future Trading Commissions, (SEC) which are supposed to regulate this activity; #DO_NOT HAVE THE #COMPUTER_CAPACITY TO #EVEN "MONITOR" IN #REAL_TIME?
* Black Monday Crash in 1977 | #Flash_Crash in a fraction of a second.
TASTINGTRAFFIC LLC Invented #HFT (High Frequency Trading) that this government and main stream news has not even mentioned the term SINCE 2007?? --bc it’s #STOLEN_SOFTWARE from our #Company (WEBTRAFFICBROKERS.COM AKA HIS ENTERPRISES INC.) btw 1999-2007. with MASSIVE PROOF now powering USA Stock Markets behind the scenes.
This did not happen bc of bullshit Trump Tariffs. Majority of Fortune 500 companies had already BETRAYED the USA for China 2 decades ago. The Tariffs was the FINAL STAKE IN THE VAMPIRES (ELITES) HEARTS WHO JUST NEEDED ONE MORE REASON TO ABANDON THE USA. Nothing to do with a 34 time loser of 34 convicted felonies!
Just ask AT&T.net (#ATT.COM). We bought their EXPIRED domain name early 2000's in a millisecond when they allowed their OWN domain NAME to EXPIRE for #not_paying their #RENT/lease. (before the #redemption_period was implemented and was policy ;)
#Hanging the #Carrot and MANIPULATING Markets at the same time. (Creating a Hope of Gain; Fear of Loss Scenario;)
In fact, this software can go back in time..(like a tape recorder: Stop, Play, Rewind and Forward within 1 millisecond intervals) like #Back to the #Future to #PREDICT (aka #SURE_BET) what they already know.. See attached images..
As Mentioned above folks we were able to see this fraud bc you need to actually #RUN_REAL_TRADES through the software to #DIAL IN the #ALGORITHMS to #CONCEAL ALL TRADES TO THE NAKED EYE >> and is #Goooooooal!
CONNECT Today for EARLY #INVITE. TastingTraffic LAUNCHING SOON!
WELCOME TO THE FUTURE OF ADVERTISING! | If it Tastes Good, You Gotta LOVE IT! (Patent Pending).
Upon launch all will be notified.
* Software Architect (PhD) Supervisor -25 years 100K PMS hours * EXPERT BLACK BOX TESTER * Founder of SEO (Search Engine Optimization) * Founder of RTB (Real Time Bidding) * Founder of HFT (High Frequency Trading)
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.
For a long time, I didn't know exactly how the Fundamental Theorem of Arithmetic (unique prime factorization) was proved from first principles.
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.
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". 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). 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. 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. 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).
Can't #deny what never happened and mustn't #accuse without #proof/if disproved (which still you do).
We #condemn depraved #genocide apologists and are not crazy enough to believe that you would ever #condemn yourself for tolerating, justifying or even celebrating #rape.
#SELF_PRESERVATION = 100% #HATE! CONTRADICTORY TO THE ENTIRE 10 #COMMANDMENTS! IN THE OLD TESTAMENT. 1 COMMANDMENT THAT COVERS ALL "LOVE ONE ANOTHER" NOT "#MURDER OTHERS WOMEN AND CHILDREN!"
About 60,000 #African_Migrants have #arrived in Israel since 2006, fleeing unrest in their home countries. But upon arrival in the ostensibly democratic country, the migrants have faced intense persecution and have been branded as "infiltrators" by right-wing politicians and activists.
DISCLAIMER: We Don't Cover the News | We Cover the 'Way' the #News is #COVERED_UP!
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By using Bitcoin you are basically #forfeiting your #right_to_anonymity and allowing Centralized Banks and Centralized Governments to track and trace all transactions of those funds just like #SWIFT payment services. Aka #Bank_Wire_Transfers that runs on SWIFT Software Technology and are NOT #Anonymous either.
Every transaction is recorded by Governments and world banks #EXCEPT FOR GOVERNMENTS AND OR CENTRAL BANKS.
What is good for the #Goose is not good for the #Gander = double standards!
GOVERNMENTS AND CENTRAL BANKS ARE THE ONLY ONES GRANTED 100% #ANONYMITY ON #BLOCKCHAIN. Once your funds are in Blockchain they will be tracked & Traced by Governments.
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* Software Architect (PhD) Supervisor -25 years 100K PMS hours * EXPERT BLACK BOX TESTER * Founder of SEO (Search Engine Optimization) * Founder of RTB (Real Time Bidding) * Founder of HFT (High Frequency Trading)
A proof quarter (notice the S) and a cicada at the carwash, lol.
We got change from a carwash in Durham -- $8 IN QUARTERS. I'm less mad about that now. Fun find that won't grade well. Desperate times call for cracking open your proof sets.
5-year investigation into "Havana Syndrome" mystery confirms what we already suspected:
#Russia n intelligence using a new weapon to cause permanent neurological damage to high-ranking #US#intelligence /law enforcement officials ...*AND CLOSE FAMILY MEMBERS.* IN USA.
"The (mistaken) idea seems to be that any hypothesis—no matter how bigoted—can be safely postulated and tested because the ‘scientific method’ weeds out untruths and leave the truths stand. This, however, overlooks two important false assumptions: that hypotheses themselves are value neutral, and that we have unlimited resources to debunk misconceived ideas."