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	Steinhaus–Moser notation - Wikipedia, the free encyclopedia
		In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers.
		It is an extension of Steinhaus's polygon notation.
		Moser's number is the number represented by "2 in a megagon", where a "megagon" is a polygon with "mega" sides.
	en.wikipedia.org /wiki/Steinhaus-Moser_notation (332 words)

	Moser polygon notation (Site not responding. Last check: 2007-11-05)
		In mathematics, Moser's polygon notation is a means of expressing certain large numbers.
		It is the obvious extension of Steinhaus polygon notation, ie., n written in an (m+1)-gon means "n in n m-gons".
		Moser's number is "2 in a Megagon", using Steinhaus' Mega.
	bopedia.com /en/wikipedia/m/mo/moser_polygon_notation.html (86 words)

	Notation - Wikipedia, the free encyclopedia
		Big O notation, used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected
		Tensor notation is a general way to represent a gravitational field in general relativity
		Positional notation also known as place-value notation, which each position is related to the next by a multiplier of that numeral system
	en.wikipedia.org /wiki/Notation (328 words)

	Large numbers - Wikipedia, the free encyclopedia
		Scientific notation was created to handle the wide range of values which occur in scientific study.
		The range 10–1e10 brings the notation closer to ordinary scientific notation, and the notation reduces to it if the number is itself in that range (the part "10^^0@" can be dispensed with).
		Steinhaus-Moser notation; apart from the method of construction of large numbers, this also involves a graphical notation with polygons; alternative notations, like a more conventional function notation, can also be used with the same functions.
	en.wikipedia.org /wiki/Large_number (2796 words)

	SS > factoids > big numbers
		The so-called "large primes" -- useful for cryptography -- are relatively small compared to the kind of numbers that soon arise in these notations.
		In order to express general relationships, it is useful to have a rather different notation, than captures the number of sides of the polygons, and the number of repetitions of the polygons, symbolically.
		The Moser construction yields big numbers much faster than does the up-arrow notation, but there are a lot of up-arrows in the Graham number.
	www-users.cs.york.ac.uk /~susan/cyc/b/big.htm (785 words)

	Large Numbers at MROB (Site not responding. Last check: 2007-11-05)
		Usually in notation the operator is placed between the two numbers.
		This notation is elegant, powerful, relatively easy to use and covers a greater range than any other discussed on these pages, within the limits of functional formal systems.
		These numbers were constructed by Hugo Steinhaus and Leo Moser (in the late 1970's or earlier, exact date unknown) just to show that it is easy to create a notation for extremely large numbers.
	home.earthlink.net /~mrob/pub/math/largenum-3.html (2346 words)

	large numbers
		However, even this seemingly immense integer is made to look ridiculously small by the likes of more recently described numbers, such as Graham's number, the Mega, and the Moser, which are so utterly vast that it takes several pages just to describe the various special notations used to represent them.
		Just as writing out a number "in full," or in place-value notation, becomes unwieldy with numbers as big as a googol, so exponentiation, in turn, endangers the world's forests if it tries to take on seriously large numbers.
		The Ackermann function and the Steinhaus-Moser notation are both equivalent to a triadic operator that is somewhat more powerful than hy(a, n, b).
	www.daviddarling.info /encyclopedia/L/large_numbers.html (1114 words)

	Britain.tv Wikipedia - Trillion
		Throughout this article, exponential or scientific notation is used.
		In science, since the 1800s, numbers have been written using the familiar "scientific notation", in which powers of ten are expressed as a ten with a numeric superscript, e.g.
		An easy way to find out scientific notation for one of the above numbers in the short scale is to take the Latin cardinal number indicated in the name (Such as 2 in 'bi'llion, 4 in 'quadri'llion, 18 in 'octodec'illion etc), then add one to it, and finally multiply the whole thing by 3.
	www.britain.tv /wikipedia.php?title=Trillion (2240 words)

	Conway chained arrow (Site not responding. Last check: 2007-11-05)
		Conway's chained arrow notation is a means of expressing certain large numbers.
		It is impossible to give a fully worked-out interesting example since at least 4 elements are required.
		However 1-, 2- and 3-length chains, which are subsumed in other notations, are expanded here as illustrated examples.
	bopedia.com /en/wikipedia/c/co/conway_chained_arrow.html (462 words)

	Large Numbers at MROB (Site not responding. Last check: 2007-11-05)
		This notation is based on Knuth's up-arrow notation.
		In this notation, three or more numbers are joined by right-arrows.
		It might be thought of as a function with a variable number of arguments, or perhaps a function whose single argument is an ordered list or vector.
	home.earthlink.net /~mrob/pub/largenum-3.html (2715 words)

	Moser polygon notation (Site not responding. Last check: 2007-11-05)
		It is the obvious extension of Steinhaus polygon notation ie.
		Moser's number is "2 in a Megagon " Steinhaus' Mega.
		Laxman, Chamber of commerce, Far from the Madding Crowd, Zhanguoce, Stratagems of the Warring States, Intrigues of the Warring States, Chronicles of the Warring States, Records of the Warring States, Annals of the Warring States, The Strategies of the Warring States, About this article.
	www.freeglossary.com /Moser_polygon_notation (430 words)

	Hyper operator - Wikipedia, the free encyclopedia
		The family has not been extended from natural numbers to real numbers in general for n>3, due to nonassociativity in the "obvious" ways of doing it.
		The other degrees do not collapse in this way, and so this family has some interest of its own as lower (perhaps lesser or inferior) hyper operators.
		I.N Galidakis, On Extending hyper4 and Knuth's Up-arrow Notation to the Reals (undated, 2006 or earlier).
	en.wikipedia.org /wiki/Hyper4 (368 words)

	Definition of Steinhaus-Moser notation (Site not responding. Last check: 2007-11-05)
		In mathematics, Moser's polygon notation is a means of expressing certain extremely large numbers.
		It has been proved that Moser's number, although extremely large, is smaller than Graham's number.
		Robert Munafo's Big Numbers (http://home.earthlink.net/~mrob/pub/math/largenum-3.html), which hints Steinhaus and Moser came up with this notation jointly in the '70s
	www.wordiq.com /definition/Steinhaus-Moser_notation (422 words)

	Knuth's up-arrow notation
		A notation for large numbers developed by the American mathematician Donald Knuth in 1976.
		Even up-arrow notation becomes cumbersome, however, when faced with staggeringly large numbers such as Graham's number.
		See also the Ackermann function, to which up-arrow notation is closely related.
	www.daviddarling.info /encyclopedia/K/Knuths_up-arrow_notation.html (177 words)

	"SOURCES IN RECREATIONAL MATHEMATICS" by David Singmaster (Site not responding. Last check: 2007-11-05)
		Steinhaus attributes the proof using the fact that a first player strategy is the negation of a second player strategy to Mycielski, but without a reference (AMM 72 (1965) 400; see also Kac, AMM 81 (1974) 577).
		Steinhaus, Sur la division pragmatique, Econometrica (supplement) 17 (1949) 315-319, is cited as the source of the problems and as giving Banach & Knaster's solution, though the material occurs in English in Econometrica 16 (1948) 101-104.
		L. Moser (AMM 55 (1948) 369) is the problem that n elements of a group of order n have a subinterval whose product is the identity.
	anduin.eldar.org /~problemi/singmast/queries.html (11864 words)

	Trillion info here at en.120-film.info (Site not responding. Last check: 2007-11-05)
		In science, since the 1800s, chiffres have dated written using the continual "scientific notation", in which clouts of ten are expressed as a ten with a numeric superscript, e.g.
		An picnic thing to treasure outside halcyon notation for singular of the aloft chiffres in the bare proportion is to take the Latin cardinal fraction allusive in the surname (Such as 2 in 'bi'llion, 4 in 'quadri'llion, 18 in 'octodec'illion etc), anon reckon up singular to it, und cert multiply the anything by 3.
		This is drained in the king-size proportion by straightforwardly multiplying the Latin numeral by 6.
	en.120-film.info /Trillion (2466 words)

	Googolplex - Free net encyclopedia
		Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.
		In pure mathematics, the magnitude of a googolplex is not as large as some of the specially defined extraordinarily large numbers, such as those written with tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation.
		Some sequences grow very quickly; for instance, the first two Ackermann numbers are 1 and 4, but then the third is ${\ ^{7625597484987}3}$ , a power tower of threes more than seven trillion high.
	www.netipedia.com /index.php/Googolplex (698 words)

	Conway chained arrow notation - TheBestLinks.com - Associativity, Ackermann function, Donald Knuth, Integers, ...
		Conway chained arrow, Conway chained arrow notation, Associativity, Ackermann...
		Conway chained arrow notation is a means of expressing certain large numbers, created by mathematician John Conway.
		It is simply a finite sequence of positive integers separated by rightward arrows, e.g.
	www.thebestlinks.com /Conway_chained_arrow.html (525 words)

	Trillion info here at en.1930-census.info (Site not responding. Last check: 2007-11-05)
		In science, since the 1800s, representations have back written using the run-of-the-mill "scientific notation", in which capabilities of ten are expressed as a ten with a numeric superscript, e.g.
		When a represents a measurement kind of than a count, SI prefixes can be used; different lips "femtosecond", not "one quadrillionth of a second.", despite ofttimes capabilities of ten are used instead of some of the very sky-high very secondary prefixes.
		An no dire straits give up to treasure cold mathematical notation for different of the beyond representations in the shortened rule is to take the Latin cardinal adumbrated in the agname (Such as 2 in 'bi'llion, 4 in 'quadri'llion, 18 in 'octodec'illion etc), thereupon count up different to it, multiply the unqualified paraphernalia by 3.
	en.1930-census.info /Trillion (2410 words)

	Large number (Site not responding. Last check: 2007-11-05)
		Beyond all these, Georg Cantor 's conception of the Absolute Infinite surely represents the absolute largest possible conceptof "large number".
		The Knuth arrow is a very simple notation thatdescribes power towers.
		For largerpower towers, it is preferrable to use hyper notation.
	www.therfcc.org /large-number-76061.html (537 words)

	MATHEWS: All Numbers Large and Beautifull
		Note that there is also a strong connection between the up-arrow notation and the famous Ackermann function which was introduced 1928 by W. Ackermann as an example of a computable function which grows faster than any primitive recursive function.
		Conway's chained arrow notation is based on Knuth's up-arrow notation and uses three or more numbers which are joined by right-arrows.
		Note also that the polygonal notation is often changed by replacing the triangles with lines, the squares with wedges, the pentagons with triangles etc.
	www.wschnei.de /number-theory/large-numbers.html (1196 words)

	Circle Notation -- from Wolfram MathWorld
		A notation for large numbers due to Steinhaus (1983).
		squares, where numbers written inside squares (and triangles) are interpreted in terms of Steinhaus-Moser notation.
		The particular number known as the mega is then defined as follows (correcting the typographical error of Steinhaus).
	mathworld.wolfram.com /CircleNotation.html (80 words)

	Steinhaus–Moser notation
		Abstract Syntax Notation number one is an international standard notation used in describing transmitted data in telecommunications.
		The formal specification notation Z is based on Zermelo-Fraenkel set theory and first order predicate logic.
		Notation software for guitar/bass tablature (4-6 strings, alternate tunings), treble/bass/drum notation, chord diagrams, and lyrics in any font.
	www.omniknow.com /common/wiki.php?in=en&term=Moser_polygon_notation (1453 words)

	how to subtract large numbers - large numbers (Site not responding. Last check: 2007-11-05)
		((27^27)^(27^27))[3](27^27)^(27^27) in your mental image Moser's the following scheme for - Rowlett 16 The naming for Large Numbers - of objects, your counts of infamy: large number phone.
		You can, of zeros U.S. and polygon notation Do Numbers Go On of the Paranormal, University of North Carolina RJN's More Digits of 111 days that don't have eleven calculated by 72 Numbers - Russ Rowlett be in awe of (2x) 110 - 110 2TIFF is (with intermediate results EIDMA/CWI Cryptography Working John Allen.
		Moser's had to say about SI prefix 10 letters Moser extended Steinhaus' notation.
	large-numbers.mirielthreadsandjules.com (1090 words)

	Trillion info here at en.19-inch-rack.info (Site not responding. Last check: 2007-11-05)
		In science, since the 1800s, numerators have archaic written using the veteran hat "scientific notation", in which virtues of ten are expressed as a ten with a numeric superscript, e.g.
		When a chiffre represents a measurement pretty than a count, SI prefixes can be used; sole orates "femtosecond", not "one quadrillionth of a second.", notwithstanding virtues of ten are used instead of some of the very prodigious 'n very bottom prefixes.
		This is drained in the faraway range by artlessly multiplying the Latin numeral by 6.
	en.19-inch-rack.info /Trillion (2464 words)

	moser - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "moser" is defined.
		Moser : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include moser: barry moser, johann jakob moser, koloman moser, steinhaus moser notation, annemarie moser prÃ¶ll, more...
	www.onelook.com /?w=moser (109 words)

	Informat.io on Large Numbers (Site not responding. Last check: 2007-11-05)
		Sometimes people refer to numbers as being "astronomically large." However, it is easy to mathematically define numbers that are much larger than those even in astronomy.
		A rule of thumb for converting between scientific notation and powers of two
		For example, aleph-null is the cardinality of the infinite set of natural numbers, and aleph-one is the next greatest cardinal number.
	www.informat.io /?title=large-numbers (2697 words)

	Search ScienceWorld
		A large number defined as where the circle notation ncirc.eps denotes "n in n squares," and triangles and squares are expanded in terms of Steinhaus-Moser notation (Steinhaus 1999, pp.
		In circle notation, ncirc.eps is defined as n in n squares, where numbers written inside squares (and triangles) are interpreted in terms of Steinhaus-Moser notation.
		Each player uses pieces of a particular color (commonly fl and red, or sometimes yellow and red), and the object is to be the first to obtain four pieces in
	scienceworld.wolfram.com /search/index.cgi?num=&q=Mega (467 words)

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