Re: Why is it so difficult?

beeworks@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 one half 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.

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

.

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