03/25/2008, 09:09 AM

Hey James,

thats really amazing how many people are out there investigating hyper (and hypo) operations; and ... how they come independently to equal results!

Your approach also first assures the law

a[n+1](b+1)=a[n](a[n+1]b)

then derives the necessary consequence that a[0]b=b+1:

However I think we dont need extra names for the left or right inverse of such a simple operation. I would call the operation increment and the rigth inverse decrement. Or maybe also successor/predecessor are acceptable names.

So you start to compete with Gianfranco! I really like his and your style of writing.

Wish you the best on your further way.

thats really amazing how many people are out there investigating hyper (and hypo) operations; and ... how they come independently to equal results!

James Knight Wrote:Ok you guys are getting closer and closer to what I have defined as zeration....

Your approach also first assures the law

a[n+1](b+1)=a[n](a[n+1]b)

Quote:Left to Right is the the Pluse One LAw

x[n](x[n+1](b)) = x[n+1](b+1)

VOILA!

then derives the necessary consequence that a[0]b=b+1:

Quote:x [n-1] (x[n](b-1)) = x [n] (b)

Substituting n = 1 and y = x+b -1

Definition 1

x [0] y = y + 1

However I think we dont need extra names for the left or right inverse of such a simple operation. I would call the operation increment and the rigth inverse decrement. Or maybe also successor/predecessor are acceptable names.

Quote:Ok that leaves the exciting right inverse!!!

Since last fall, I had my doubts over the commutativity of zeration as well as the discontinuity. I have spent numerous hours redoing laws and being frustrated. Ok now I would like to present to you

Knightation or Nitation (struggling on what to call it...)

Knightation is the Right Inverse of Zeration.

The Operator J is used to refer to Knightation (it's supposed to look like an ear lobe idea)

if x o y = z then

y = z J x

Definition 2

x J y = x - 1

Quote:Well I hope you have gained something from this or have been entertained by my random jokes.

So you start to compete with Gianfranco! I really like his and your style of writing.

Quote:Also I am a computer programmer and I am going to soon start a program that will compute and graph hyperoperations. Anyway, I am sooooo happy right now because I got accepted to the University of Waterloo!! Soo tired!

Wish you the best on your further way.