Re: Why is it so difficult?

On Aug 10, 11:44 am, "I.N. Galidakis" <morph...@xxxxxxxxxxxx> wrote:
beewo...@xxxxxxxxxxx wrote:
On Aug 10, 3:56 am, mike3 <mike4...@xxxxxxxxx> wrote:
Hi.

Why is it so difficult, anyway, to extend tetration to real numbers?
For example, why is it easier to define 2 raised to the one half
power, but hard to define 2 tetrated to the onehalf tower?

Given a, a^(1/2) = b is defined as the (positive) b such that b^2 =
a. Try doing the same with tetration.

It can be done (with some effort). The process introduces the notion of
Hyperroot:http://ioannis.virtualcomposer2000.com/math/exponents3.html

However this definition cannot be used in defining x^^(m/n), because m and n do
not commute in tetration.

However, the notion of the hyperroot stands, by itself.


However why would it then be reasonable to assume that
^(1/n) x = inverse(^n x) (or hyperroot_n(x)), anyway?
Why might not you need to tetrate to something else to
get inverse(^n x)? Since in general ^m(^n x) != ^(mn) x.

- MO

--
I.N. Galidakis ---http://ioannis.virtualcomposer2000.com/


.

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