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Topic: Hyper4

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	Large Numbers at MROB
		To the best of my knowledge, the hyper4 operator has not been extended to real numbers, as the common operators are.
		A common question about hyper4 is how to perform an inverse operation —; the equivalent of a "hyper4 logarithm" or a "hyper4 root".
		The "hyper4 root" can be evaluated for fixed integer "root" values using Newton's method.
	home.earthlink.net /~mrob/pub/math/largenum-3.html (1867 words)

	Hyper4 - MedPort-Lexikon
		Was halten Sie von der Aussage der privaten Krankenkassen, dass durch die Gesundheitsreform Gebührenerhöhungen von mindestens 10?% notwendig sind?
		hyper4 ist eine mathematische Notation zur Beschreibung von "Potenz-Türmen" und großen Zahlen durch eine Erweiterung der herkömmlichen Operatoren für die Addition, Multiplikation und Potenzierung.
		hyper4 wird auch bezeichnet als Tetration oder Superpotenz; es gibt dafür auch die Notation $\operatorname{hyper4}(a,b)={}^{b}a .$
	www.medport.de /lexikon/index.php/Hyper4 (329 words)

	hyper4 is an notation that describes power towers...
		hyper4 is an notation that describes power towers...
		"hyper4" is an notation that describes power towers and large numbers, in terms of an extension of standard operators.
		Known aliases for hyper4 include "tetration", "superpower", "superdegree", and "powerlog"; other notation, \operatorname)\times a define a_(n+1)b = a+b But this suffers a kind of collapse, failing to form the "power tower" traditionally expected of hyper4: a_(a^(n)b suddenly diverge for "n>3"?
	www.geodatabase.de /Hyper4 (243 words)

	Hyper4
		hyper4 is a fourth level dyadic (binary) mathematic operation involving exponentiation of exponents.
		The hyper4 has not been extended to real numbers as addition (1st level dyadic operation), multiplication (2nd level) and exponentiation (3rd level) have.
		Hyper4 is essentially equivalent to a↑↑b in Knuth's up-arrow notation.
	www.ebroadcast.com.au /lookup/encyclopedia/hy/Hyper4.html (115 words)

	Station Information - Hyper4
		hyper4 is an notation that describes power towers and large numbers, in terms of an extension of standard operators.
		The family has not been extended to real numbers for n>3, due to nonassociativity in the "obvious" ways of doing it.
		Known aliases for hyper4 include tetration, superpower, superdegree, and powerlog; other notation, hyper4(a,b)=
	www.stationinformation.com /encyclopedia/h/hy/hyper4.html (220 words)

	Hyper operator - Wikipedia, the free encyclopedia
		For n = 4 we have hyper4 or tetration, super-exponentiation or power towers in terms of an extension of standard operators:
		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.
		This is because of a symmetry called associativity that's defined into + and × (see field) but which ^ lacks.
	en.wikipedia.org /wiki/Hyper4 (368 words)

	Hyper4
		hyper4 is an notation that describes power towers and large numbers, in terms of an extension of standard operators.
		The family has not been extended to real numbers for n>3, due to nonassociativity in the "obvious" ways of doing it.
		Known aliases for hyper4 include tetration, superpower, superdegree, and powerlog; other notation, hyper4(a,b)=
	www.guajara.com /wiki/en/wikipedia/h/hy/hyper4.html (244 words)

	hyper4@Everything2.com
		The hyper4 has not been extended to real numbers as addition (1st level dyadic operation), multiplication (2nd level) and exponentiation (3rd level) have.
		Alternate names for hyper4 can include: tetration, superpower, superdegree, and powerlog.
		This concept can be extended to the fifth degree and beyond as well, however each definition becomes recursive upon the last one...
	www.everything2.com /?node_id=1403553 (167 words)

	Further Lynz Explanation and the Clarkkkkson
		The hyper4 of 4 and 5 is 4^^5=(((4^4)^4)^4)^4 or in other words, 4 to the power itself, with five 4's.
		Hyper4 of 4 and 3 = 4^^3 = 4^4^4 = 4294967296
		Note that you do the operation 4 times, you are in fact doing it on 5 numbers (because the one you started with counts, doesn't it?), which is where the 5 fits in.
	lab6.com /old/school/yearbook/clarkkkkson.html (1489 words)

	hyper4 is an notation that describes power tower power towers...
		hyper4 is an notation that describes power tower power towers...
		"hyper4" is an notation that describes power tower power towers and large number large numbers, in terms of an extension of standard operator operators.
		Known aliases for hyper4 include "tetration", "superpower", "superdegree", and "powerlog"; other notation, \operatorname)\times a define a_(n+1)b = a+b But this suffers a kind of collapse, failing to form the "power tower" traditionally expected of hyper4: a_(a^(n)b suddenly diverge for "n>3"?
	www.biodatabase.de /Hyper4 (280 words)

	Hyper4 - infos.aus-germanien.de
		hyper4 ist eine mathematische Notation zur Beschreibung von "Potenz-Türmen" und großen Zahlen durch eine Erweiterung der herkömmlichen Operatoren für die Addition, Multiplikation und Potenzierung.
		hyper4 wird auch bezeichnet als Tetration oder Superpotenz; es gibt dafür auch die Notation $\operatorname{hyper4}(a,b)={}^{b}a .$
		Lynz and the ClarkkkksonOn extending hyper4 to nonintegers
	infos.aus-germanien.de /Hyper4 (305 words)

	large numbers
		Tetration goes by various other names including superpower, superdegree, and, the one used most commonly in mathematical circles and also here from now on, hyper4.
		x a (b terms), the hyper4 of a and b is represented as a
		Alternatively, the hyper4 operator can be represented in Knuth's up-arrow notation as a
	www.daviddarling.info /encyclopedia/L/large_numbers.html (1114 words)

	A Continuous Extension for the Hyper4 Operator
		The problem has been known under the name "continuous extension of the hyper4 operator", "continuous extension of the Ackermann function", "continuous extension of the hyperexponentiation functions", and under various different names.
		However, this is a minor nuisance, because it is rather the definition of the hyperroot which may be considered deviant in this case.
		For an infinitely differentiable extension of hyper4, consult
	ioannis.virtualcomposer2000.com /math/exponents4.html (1578 words)

	Delta Function
		Firstly, it’s very probable that someone else has already formulated this, but I haven’t seen it, and I didn’t know what else to call it, so I called it delta.
		(Actually, look up the hyper4 operator for some proper maths on the subject).
		And this has nothing to do with the dirac delta function.
	www.maths.tcd.ie /~icecube/delta.php (217 words)

	Tetration - Wikipedia, the free encyclopedia
		Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation.
		I.N. Galidakis, On extending hyper4 to nonintegers (undated, 2006 or earlier) (A simpler, easier to read review of the next reference)
		Robert Munafo, Extension of the hyper4 function to reals (An informal discussion about extending tetration to the real numbers.)
	en.wikipedia.org /wiki/Super-exponentiation (1046 words)

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