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Googolplex
A googolplex is the number 10, or equivalently, 10 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 . Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes. History In 1920, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term ''googol'', which is 10, and then proposed the further term ''googolplex'' to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition because "different people get tired at different times and it would never do to have Primo Carnera, Carnera [be] a better mathematician than Albert Einstein, Dr. Einstein, simply because he had more endurance and could write for longer". It thus became standardized to 10(10100) = 1010100, due to the associativity, right-associativity of exponentiation. Size A typical book can be printed with 10 zeros ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Names Of Large Numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. These naming procedures are based on taking the number ''n'' occurring in 103''n''+3 (short scale) or 106''n'' (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix ''-illion''. Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as ''10'' with a numeric superscript. Indian English does not use millions, but has its own system of large numbers including lakhs and crores. English also has many words, such as "zillion", used informally to mean large but unspecified am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Kasner
Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in the sciences at Columbia University. Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. Differential geometry was his main field of study. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon. Education Kasner's 1899 PhD dissertation at Columbia University was titled ''The Invariant Theory of the Inversion Group: Geometry upon a Quadric Surface''; it was published by the American Mathematical Society in 1900 in their ''Transactions''. Googol and googolplex Kasner is perhaps best remembered today for introducing the term "googol." In order to pique the interest of children, Kasner sought a name for a very large number: one foll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Numbers
Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics. They are typically large positive integers, or more generally, large positive real numbers, but may also be other numbers in other contexts. Googology is the study of nomenclature and properties of large numbers. In the everyday world Scientific notation was created to handle the wide range of values that occur in scientific study. 1.0 × 109, for example, means one billion, or a 1 followed by nine zeros: 1 000 000 000. The reciprocal, 1.0 × 10−9, means one billionth, or 0.000 000 001. Writing 109 instead of nine zeros saves readers the effort and hazard of counting a long series of zeros to see how large the number is. Examples of large numbers describing everyday real-world objects include: * Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Googol
A googol is the large number 10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Etymology The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner. He may have been inspired by the contemporary comic strip character Barney Google. Kasner popularized the concept in his 1940 book '' Mathematics and the Imagination''. Other names for this quantity include ''ten duotrigintillion'' on the short scale, ''ten thousand sexdecillion'' on the long scale, or ''ten sexdecilliard'' on the Peletier long scale. Size A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a ches ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Googol
A googol is the large number 10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Etymology The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner. He may have been inspired by the contemporary comic strip character Barney Google. Kasner popularized the concept in his 1940 book '' Mathematics and the Imagination''. Other names for this quantity include ''ten duotrigintillion'' on the short scale, ''ten thousand sexdecillion'' on the long scale, or ''ten sexdecilliard'' on the Peletier long scale. Size A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a ches ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperoperation
In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called ''hyperoperations'' in this context) that starts with a unary operation (the successor function with ''n'' = 0). The sequence continues with the binary operations of addition (''n'' = 1), multiplication (''n'' = 2), and exponentiation (''n'' = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the ''n''th member of this sequence is named by Reuben Goodstein after the Greek prefix of ''n'' suffixed with ''-ation'' (such as tetration (''n'' = 4), pentation (''n'' = 5), hexation (''n'' = 6), etc.) and can be written as using ''n'' − 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by: :a = \underbrace_,\quad n \ge 2 It may also be defined according to the recursion rule part of the de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graham's Number
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 such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. 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 ^. Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics And The Imagination
''Mathematics and the Imagination'' is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received several glowing reviews. Special publicity has been awarded it since it introduced the term googol for 10100, and googolplex for 10googol. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages. Reviews According to I. Bernard Cohen, "it is the best account of modern mathematics that we have", and is "written in a graceful style, combining clarity of exposition with good humor". According to T. A. Ryan's review, the book "is not as superficial as one might expect a book at the popular level to be. For instance, the description of the invention of the term ''googol'' ... is a very serious attempt to show how misused is the term ''infinite'' when applied to large and finite numbers." By 1941 G. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Personal Voyage
''Cosmos: A Personal Voyage'' is a thirteen-part, 1980 television series written by Carl Sagan, Ann Druyan, and Steven Soter, with Sagan as presenter. It was executive-produced by Adrian Malone, produced by David Kennard, Geoffrey Haines-Stiles, and Gregory Andorfer, and directed by the producers, David Oyster, Richard Wells, Tom Weidlinger, and others. It covers a wide range of scientific subjects, including the origin of life and a perspective of our place in the universe. Owing to its bestselling companion book and soundtrack album using the title, ''Cosmos'', the series is widely known by this title, with the subtitle omitted from home video packaging. The subtitle began to be used more frequently in the 2010s to differentiate it from the sequel series that followed. The series was first broadcast by the Public Broadcasting Service in 1980, and was the most widely watched series in the history of American public television until '' The Civil War'' (1990). As of 2009, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associativity
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: \begin (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24 . \end Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primo Carnera
Primo may refer to: People *DJ Premier (born 1966), hip-hop producer, sometimes goes by nickname Primo * Primo Carnera (1906–1967), Italian boxer, World Heavyweight champion 1933–1934 * Primo Cassarino (born 1956), enforcer for the Gambino crime family * Primo Colón (born 1982), ring name of professional wrestler Eddie Colón, multiple tag team champion in the WWE *Primo Conti (1900–1988), Italian Futurist artist *Primo Levi (1919–1987), Jewish Italian chemist, Holocaust survivor, and author *Primo Miller (1915–1999), American football player *Primo Riccitelli (1880–1941), Italian composer *Primo Zamparini (born 1939), Italian bantamweight Olympic and professional boxer *Primo Brown (1976–2016), Italian rapper *Primož Brezec (born 1979), Slovenian professional basketball player * Al Primo (1938–2022), American television news executive credited with creating the ''Eyewitness News'' format * Giancarlo Primo (1924–2005), Italian basketball player and coach * Josh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
