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Sorry for telling it straigth away. The function f(x) = A ^ B ^ x equals the function f(x) = A ^ (B * x). Try it in a spreadsheet, if you don't believe it. A double exponential function is just an exponential function as any other. The reason that f(x) = A ^ (B * x) grows faster than f(x) = A ^ x is
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Pretty much a linguistic distinction without a difference IMO. It looks like "doubly exponential" is used to describe expressions with stacked exponentials, as in the N(y) in the
Theoretical biology section, while "double exponential" means a more specific function. In other words one phrase is used
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Because a googolplex (note the spelling) is 10, and 10 to the 1000th is just 10. Take the common logarithm of both sides and you get 10 and 1000 = 10 respectively: the former is obviously much larger than the latter. (Or if it isn't obvious yet, do it again to get 100 and 3, where there can be no
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Just a note for eagle-eyed editors out there: the reading reference I gave has a different date than the text in the page linked to claims. The page is wrong, the correct date is 1973. This can be verified with an index of
Fibonacci Quarterly if desired.
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The two terms are almost equally represented in the article, with their clustering suggesting different editors prefer one or the other version. Shouldn't they be unified, possibly with some explanation in the lead para about their equivalence?
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as an adjective and the other is used as a noun. Having both phrases makes sense in terms of readability; it does make the scope of the article a bit vague but with so little material to work with this seems harmless. --
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I'm not a mathematician, but should that read "log(log(x))"? Doesn't "ln" imply the natural log, log using the base e, which would imply that the a and b of the double exponential function as given woudl be equal to e?
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I would say "double exponential". I don't think you would call its inverse "doubly logarithmic". I would say "It is a double exponential function" but "the function is doubly exponential".
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that we are multiplying the exponent by a constant B. The statement, that a double exponential function is growing faster than an exponential function just doesn't make any sense.
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Most of the contain of the section "Data structures" is irrelevant to this article. If it is notable enough for
Knowledge, it should appear in separate articles in
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I agree with Bubba. It should be “a double exponential function” (a function containing a double exponential) but “a function that is doubly exponential”.
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This article needs to explain the order of calculation of exponentials. It is not made clear here why a googleplex is larger than 10 to the 1000th.
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I made some modifications to reflect the correct interpretation of powers of powers, but the error is repeated across the whole page...
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doubt as to which is larger.) You do power towers from the right, so 10 means 10 and not (10) (which indeed equals 10).
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is not explained in this article, but it is commonly agreed upon (at least among professional mathematicians) that
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The article currently reads, "The inverse of the double exponential function is the double logarithm ln(ln(x))."
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Observe that the two functions f(x) = A ^ (B ^ x) and g(x) = (A ^ B)^x are not identical. The notation
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I've edited the article, so that the meaning of the notation is explained.
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Log log is probably better. Not a big deal, I changed it. -
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