🐍justacoolguy🐍⚛

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Based! 🔥 ! Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers introduced as effective bounds in mathematics, such as Skewes's bound, which in turn is much larger than a googolplex. Graham's number is so large that the observable universe is far too small to contain its ordinary digital representation, assuming that each digit occupies one Planck volume. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus, Graham's number cannot be expressed even by physical universe-scale power towers of the form a b c ⋅ ⋅ ⋅ {\displaystyle a^{b^{c^{\cdot ^{\cdot ^{\cdot }}}}}}, even though Graham's number is indeed a power of three. However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers, the sequence of which grows faster than any computable sequence. Though too large to ever be computed in full, the sequence of digits of Graham's number can be computed explicitly via simple algorithms; the last 10 digits of Graham's number are ...2464195387.[1] Using Knuth's up-arrow notation, Graham's number is g 64 {\displaystyle g_{64}},[2] where g n = { 3↑↑↑↑3, if n=1 and 3 ↑ g n − 1 3, if n≥2. {\displaystyle g_{n}={\begin{cases}3\uparrow \uparrow \uparrow \uparrow 3,&{\text{if }}n=1{\text{ and}}\\3\uparrow ^{g_{n-1}}3,&{\text{if }}n\geq 2.\end{cases}}} Graham's number was used by Graham in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in Scientific American, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was described in the 1980 Guinness Book of World Records, adding to its popular interest. Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem. Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number was derived have since been proven to be valid. Example of a 2-colored 3-dimensional cube containing one single-coloured 4-vertex coplanar complete subgraph. The subgraph is shown below the cube. This cube would contain no such subgraph if, for example, the bottom edge in the present subgraph were replaced by a blue edge – thus proving by counterexample that N* > 3. Graham's number is connected to the following problem in Ramsey theory: Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured complete subgraph on four coplanar vertices? In 1971, Graham and Rothschild proved the Graham–Rothschild theorem on the Ramsey theory of parameter words, a special case of which shows that this problem has a solution N*. They bounded the value of N* by 6 ≤ N* ≤ N, with N being a large but explicitly defined number N = F 7 ( 12 ) = F ( F ( F ( F ( F ( F ( F ( 12 ) ) ) ) ) ) ) , {\displaystyle N=F^{7}(12)=F(F(F(F(F(F(F(12))))))),} where F ( n ) = 2 ↑ n 3 {\displaystyle F(n)=2\uparrow ^{n}3} in Knuth's up-arrow notation; the number is between 4 #usa #china #russia #european #politics

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#usa #russia #based #china #politics Based! 😎🔥! Tokyo Ghoul (Japanese: 東京喰種トーキョーグール, Hepburn: Tōkyō Gūru) is a Japanese dark fantasy manga series written and illustrated by Sui Ishida. It was serialized in Shueisha's seinen manga magazine Weekly Young Jump from September 2011 to September 2014, with its chapters collected in 14 tankōbon volumes. The manga has been licensed for English release in North America by Viz Media. Tokyo Ghoul First tankōbon volume cover, featuring Ken Kaneki 東京喰種トーキョーグール (Tōkyō Gūru) Genre Dark fantasy[1] Supernatural thriller[2] Manga Written by Sui Ishida Published by Shueisha English publisher NA: Viz Media Imprint Young Jump Comics Magazine Weekly Young Jump Original run September 8, 2011 – September 18, 2014 Volumes 14 (List of volumes) Further information icon Anime and manga portal The story is set in an alternate version of Tokyo where humans coexist with ghouls, beings who look like humans but can only survive by eating human flesh. Ken Kaneki is a college student who is transformed into a half-ghoul after an encounter with one of them. He must navigate the complex social and political dynamics between humans and ghouls while struggling to maintain his humanity. A prequel, titled Tokyo Ghoul [Jack], ran online on Jump Live in 2013, with its chapters collected in a single tankōbon volume. A sequel, titled Tokyo Ghoul:re, was serialized in Weekly Young Jump from October 2014 to July 2018, its chapters were collected in 16 tankōbon volumes. A 12-episode anime television series adaptation produced by Pierrot, aired on Tokyo MX from July to September 2014. A 12-episode second season, titled Tokyo Ghoul √A (pronounced Tokyo Ghoul Root A), which follows an original story, aired from January to March 2015. A live-action film based on the manga was released in Japan in July 2017, with a sequel being released in July 2019. An anime adaptation based on the sequel manga, Tokyo Ghoul:re, aired for two seasons; the first from April to June 2018, and the second from October to December 2018. By January 2021, Tokyo Ghoul had over 47 million copies in circulation worldwide, making it one of the best-selling manga series of all time. Tokyo Ghoul is set in an alternate reality where ghouls, creatures that look like normal people but can only survive by eating human flesh, live among the human population in secrecy, hiding their true nature in order to evade pursuit from the authorities. Ghouls have powers including enhanced strength, speed, endurance and regenerative abilities—a regular ghoul produces 4–7 times more kinetic energy in their muscles than a normal human; they also have several times the RC cells, a cell that flows like blood and can become solid instantly. A ghoul's skin is resistant to ordinary piercing weapons, and it has at least one special predatory organ called a Kagune (赫子), which it can manifest and use as a weapon during combat. Another distinctive trait of ghouls is that when they are excited or hungry, the color of their sclera in both eyes turns black and their irises red. This mutation is known as kakugan (赫眼; 'red eye'). A half-ghoul can either be born naturally as a ghoul and a human's offspring, or artificially created by transplanting some ghoul organs into a human. In both cases, a half-ghoul is usually much stronger than a pure-blood ghoul. In the case of a half-ghoul, only one of the eyes undergoes the "red eye" transformation. Natural born half-ghouls are very rare, and creating half-ghouls artificially initially has a low success rate. There is also the case of half-humans, hybrids of ghouls and humans that can feed like normal humans and lack a Kagune while possessing enhanced abilities, like increased reaction speeds, but shortened lifespans. Naturally born half-ghouls can also eat like normal humans or full ghouls. Plot edit Eeeeeeeeeeeeeeeeeeeeeeeeeeee Eeeeeeeeeeeeeeeeeeeeeeeeeeee Eeeeeeeeeeeeeeeeeeeeeeeeeeee Eeeeeeeeeeeeeeeeeeeeeeeeeeee Eeeeeeeeeeeeeeeeeeeeeeeeeeeefrreedeedddddddeeeeeeeerrre

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Based! 🔥 😎 #usa #russia #china #based #politics The Western world, also known as the West, primarily refers to various nations and states in Europe, Northern America, and Australasia; with some debate as to whether those in the former Soviet Union, Greece and Eastern Europe, and Latin America, even though its cultures are derived from Iberian cultures[1][2], also constitute the West.[3][4] The Western world likewise is called the Occident (from Latin occidens 'setting down, sunset, west') in contrast to the Eastern world known as the Orient (from Latin oriens 'origin, sunrise, east'). Definitions of the "Western world" vary according to context and perspectives; the West is an evolving concept made up of cultural, political, and economic synergy among diverse groups of people, and not a rigid region with fixed borders and members.[5] The Parthenon in Athens The Roman Forum in Rome Ancient Greco-Roman world forms the foundation of the modern Western world Ancient Greece and Rome are widely regarded by Westerners as the birthplaces of Western civilization.[6] A geographical concept of the West started to take shape in the 4th century CE when Constantine, the first Christian Roman emperor, divided the Roman Empire between the Greek East and Latin West. The Eastern Roman Empire, later called the Byzantine Empire, continued for a millennium, while the Western Roman Empire lasted for only about a century and a half. Significant theological and ecclesiastical differences led Western Europeans to consider the Christians in the Byzantine Empire as heretics. In 1054 CE, when the church in Rome excommunicated the patriarch of Byzantium, the politico-religious division between the Western church and Eastern church culminated in the Great Schism or the East–West Schism.[7] Even though friendly relations continued between the two parts of Christendom for some time, the crusades made the schism definitive with hostility.[8] The West during these crusades tried to capture trade routes to the East and failed, it instead discovered the Americas.[9] In the aftermath of the European colonization of the Americas, primarily involving Western European powers, an idea of the "Western" world, as an inheritor of Latin Christendom emerged.[10] According to the Oxford English Dictionary, the earliest reference to the term "Western world" was from 1586, found in the writings of William Warner.[11] The countries that are considered constituents of the West vary according to perspective rather than their geographical location. Countries like Australia and New Zealand, located in the Eastern Hemisphere are included in modern definitions of the Western world, as these regions and others like them have been significantly influenced by the British—derived from colonization, and immigration of Europeans—factors that grounded such countries to the West.[12] Depending on the context and the historical period in question, Russia has sometimes been seen as a part of the West, and at other times juxtaposed with it, as well as endorsing anti-Western sentiment.[13][14][15] In the New World, the United States became more prominently featured in the conceptualizations of the West as it rose as a great power, amidst the development of communication–transportation technologies like the telegraph and railroads "shrinking" the distance between both the Atlantic Ocean shores.[13] Additionally, even though the various national cultures of Latin America share a common Western cultural basis—derived from colonization, and immigration of Europeans— originating in Spain and Portugal[1][2], there was debate among some in the 1960s as to whether Latin America as a whole is in a category of its own.[16] This is mostly due to the various cultural influences that Latin American cultures have received from Indigenous peoples of the Americas, as well as African peoples, not unlike other postcolonial cultures from the Americas, such as the Unit