02/21/2008, 11:52 PM
KAR Wrote:Я согласен с Вами. My operation is not zeration, even if it does exhibit some similar properties, such has having identity element asquickfur Wrote:[...]Yes, you are right, that it is possible to construct this operator. It is a classical homomorphism of addition with using function exp(x). I researched in 90th years application of this operator and of some others for upgrade numerical solution systems of the differential equations. Good the outcome was with a homomorphism on the basis function ln(x).
Eventually, I came upon the definition:. As you can verify,
.
However, this operator (a homomorphism of addition) is not Zeration. Moreover, application Zeration has allowed to achieve more simple algorithms of a homomorphism methods numerical solution of the differential equations and their systems. These researches are available in my monography (in Russian).
Quote:[...]Yes, it seems that any operation below addition, where some form of iteration reduces to addition, must have
If Zeration it is commutative.
The interesting thing about this, is that if we then construct inverse elements w.r.t. to #, then we must admit new numbers that lie "before"
Quote:[...]Нет ничего. As long as it gets the message across...
P.s. I bring an apology, for quality of computer translation on English.
