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.