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(07/05/2009, 07:41 PM)robo37 Wrote: My point is that x^^0 should be the same as x√x because it follows along with the pattern

yes I confirmed that already in my previous post, however only for the left-to-right tetration.

Quote:Left to right tetration is on the line of best fit as to say while right to left tetration seems to be as out of place as the whole concept of working from right to left is altogether.

What does it fit better than right-to-left tetration?

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07/05/2009, 09:21 PM
(This post was last modified: 07/05/2009, 09:37 PM by robo37.)
(07/05/2009, 08:10 PM)bo198214 Wrote: What does it fit better than right-to-left tetration?

Do you mean

why does it fit better than right-to-left tetration? As I said, it inherits more characteristics than the previous hyper operations.

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07/05/2009, 09:42 PM
(This post was last modified: 07/05/2009, 09:43 PM by bo198214.)
(07/05/2009, 09:21 PM)robo37 Wrote: (07/05/2009, 08:10 PM)bo198214 Wrote: What does it fit better than right-to-left tetration?

Do you mean why does it fit better than right-to-left tetration? As I said, it inherits more characteristics than the previous hyper operations.

No question was "what", i.e. give me some properties that left-to-right tetr. does satisfy which is not satisfied by right-to-left tetration, but which you would expect from a tetration.

As nuninho already wrote you can replace the roots by logarithms for the right-to-left tetration of negative values, then however tet(-2) is not defined, but this is not really a drawback.

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07/05/2009, 10:04 PM
(This post was last modified: 07/05/2009, 10:05 PM by robo37.)
(07/05/2009, 09:42 PM)bo198214 Wrote: give me some properties that left-to-right tetr. does satisfy which is not satisfied by right-to-left tetration

Well other than the facts that x^^0 should be x√x and (x^^y)√(x^^z) should be x^^(z-y) that I've already mentioned......... I don't know......... I'm guessing that with a series of numbers generated by left to right tetration there would be a easy to find out the nth term and with right to left tetration there wouldn't, but I haven’t tried that out yet.

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(07/05/2009, 10:04 PM)robo37 Wrote: Well other than the facts that x^^0 should be x√x and (x^^y)√(x^^z) should be x^^(z-y)

Something that "should be" can not be a fact

And it is not satisfiable.

It is not even true that (x^^y)^(x^^z) = x^^(y+z).

One can prove that any suitable operation ^^ which satisfies this equation is trivial, e.g. x^^y=1.

Neither left-to-right tetration nor right-to-left tetration nor symmetric/balanced tetration satisfies this anticipated property.

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sorry I mistaked. I edit from "... X = oo" to "... X = -oo" in my post #6 and from x^(x^n) to "x^(x^(n-1))" in my post #8.