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Googolplex
A googolplex is the large number 10, or equivalently, 10 or . Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2 ×5. 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 Carnera ea better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer". It thus became standardized to 10(10100) = 1010100, due to the right-associativity of exponentiation. Size A typical book can be printed with 10 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 such books to print all the zeros of a googolp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Names Of Large Numbers
Depending on context (e.g. language, culture, region), some large numbers have names that allow for describing large quantities in a textual form; not mathematical. For very large values, the text is generally shorter than a decimal numeric representation although longer than scientific notation. 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 ... [...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, far beyond those encountered in everyday life—such as simple counting or financial transactions—play a crucial role in various domains. These expansive quantities appear prominently in mathematics, cosmology, cryptography, and statistical mechanics. While they often manifest as large positive integers, they can also take other forms in different contexts (such as P-adic number). Googology delves into the naming conventions and properties of these immense numerical entities. Since the customary, traditional (non-technical) decimal format of large numbers can be lengthy, other systems have been devised that allows for shorter representation. For example, a billion is represented as 13 characters (1,000,000,000) in decimal format, but is only 3 characters (109) when expressed in exponential format. A trillion is 17 characters in decimal, but only 4 (1012) in exponential. Values that vary dramatically can be represented and compared graphically via logarithmic sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Googol
A googol is the large number 10100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeros: 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. Its systematic name is ten duotrigintillion ( short scale) or ten sexdecilliard ( long scale). Its prime factorization is 2100 × 5100. Etymology The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of American 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 (commonly used in English speaking countries), ''ten thousand sexdecillion'' on the long scale, or ''ten sexdecilliard'' on the Peletier long scale. Size A googol has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Number
Large numbers, far beyond those encountered in everyday life—such as simple counting or financial transactions—play a crucial role in various domains. These expansive quantities appear prominently in mathematics, cosmology, cryptography, and statistical mechanics. While they often manifest as large positive integers, they can also take other forms in different contexts (such as P-adic number). Googology delves into the naming conventions and properties of these immense numerical entities. Since the customary, traditional (non-technical) decimal format of large numbers can be lengthy, other systems have been devised that allows for shorter representation. For example, a billion is represented as 13 characters (1,000,000,000) in decimal format, but is only 3 characters (109) when expressed in exponential format. A trillion is 17 characters in decimal, but only 4 (1012) in exponential. Values that vary dramatically can be represented and compared graphically via logarithmic sca ... [...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 defi ... [...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] |
Graham's Number
Graham's number is an Large numbers, 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 Numerical digit, 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 Tetrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Chained Arrow Notation
Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6. As with most combinatorial notations, the definition is recursive. In this case the notation eventually resolves to being the leftmost number raised to some (usually enormous) integer power. Definition and overview A "Conway chain" is defined as follows: * Any positive integer is a chain of length 1. * A chain of length ''n'', followed by a right-arrow → and a positive integer, together form a chain of length n+1. Any chain represents an integer, according to the six rules below. Two chains are said to be equivalent if they represent the same integer. Let a, b, c denote positive integers and let \# denote the unchanged remainder of the chain. Then: #An empty chain (or a chain of length 0) is equal to 1. #The chain a represents the number a. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Notation
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A decimal numeral (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
