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Zeration
#31
Hey James,

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.
Reply


Messages In This Thread
Zeration - by GFR - 02/14/2008, 06:38 PM
RE: Zeration - by Ivars - 02/14/2008, 08:10 PM
RE: Zeration - by GFR - 02/14/2008, 10:41 PM
RE: Zeration - by mathamateur - 07/30/2009, 06:31 AM
RE: Zeration - by Ivars - 02/21/2008, 07:22 PM
RE: Zeration - by quickfur - 02/21/2008, 09:34 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:18 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:25 PM
RE: Zeration - by quickfur - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:12 PM
RE: Zeration - by KAR - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:52 PM
RE: Zeration - by GFR - 02/24/2008, 12:39 AM
RE: Zeration - by Ivars - 02/24/2008, 02:50 PM
RE: Zeration - by marraco - 03/20/2015, 09:59 PM
RE: Zeration - by bo198214 - 02/24/2008, 11:02 AM
RE: Zeration - by GFR - 03/19/2008, 12:40 PM
RE: Zeration - My Research / Investigation - by bo198214 - 03/25/2008, 09:09 AM
More on Zeration - by James Knight - 03/25/2008, 03:44 PM
Delta Numbers As HyperReals - by James Knight - 03/26/2008, 12:50 AM
RE: Delta Numbers As HyperReals - by Ivars - 03/26/2008, 12:15 PM
RE: Zeration - by GFR - 03/26/2008, 12:22 AM
RE: Zeration - by GFR - 04/05/2008, 08:58 PM
RE: Zeration - by Igor M - 01/14/2009, 04:04 PM
RE: Zeration - by bo198214 - 01/20/2009, 09:59 PM
RE: Zeration - by 73939 - 07/05/2010, 12:00 AM
RE: Zeration - by bo198214 - 07/05/2010, 07:37 AM
RE: Zeration - by brangelito - 07/20/2010, 05:51 PM
RE: Zeration - by bo198214 - 07/21/2010, 02:58 AM
RE: Zeration - by JmsNxn - 11/09/2011, 01:40 AM
RE: Zeration - by quickfur - 11/09/2011, 04:15 AM
RE: Zeration - by JmsNxn - 11/10/2011, 01:20 AM
RE: Zeration - by quickfur - 11/10/2011, 02:09 AM
RE: Zeration - by marraco - 03/20/2015, 09:44 AM
RE: Zeration - by marraco - 03/20/2015, 10:41 PM
RE: Zeration - by marraco - 03/21/2015, 12:35 AM
RE: Zeration - by marraco - 03/21/2015, 01:44 AM
RE: Zeration - by marraco - 03/21/2015, 04:10 AM
RE: Zeration - by MphLee - 03/21/2015, 11:53 AM
RE: Zeration - by marraco - 03/23/2015, 07:58 AM
RE: Zeration - by tommy1729 - 03/21/2015, 11:11 PM
RE: Zeration - by marraco - 03/23/2015, 08:05 AM
RE: Zeration - by marraco - 03/24/2015, 11:29 AM
RE: Zeration - by MphLee - 03/23/2015, 09:00 AM
RE: Zeration - by marraco - 03/23/2015, 01:39 PM
RE: Zeration - by MphLee - 03/23/2015, 02:31 PM
RE: Zeration - by Stanislav - 05/28/2015, 11:12 PM
RE: Zeration - by marraco - 05/29/2015, 01:33 AM
RE: Zeration - by Stanislav - 05/29/2015, 09:06 PM
RE: Zeration - by MphLee - 06/03/2015, 01:40 PM
RE: Zeration - by Stanislav - 06/04/2015, 06:44 AM
RE: Zeration - by marraco - 06/04/2015, 08:44 PM
RE: Zeration - by MphLee - 06/05/2015, 09:10 PM
RE: Zeration - by Stanislav - 09/09/2015, 10:04 PM
RE: Zeration - by Stanislav - 10/31/2016, 02:57 PM

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