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Generalized recursive operators
#40
It would appear that we have our work cut out for us, in defineing higher operators, addition, multiplication, exponentiation, tetration, pentation, hexation....ultration.

What I am interested in in is generalized triadic operators, for higher operators, you know y=x[w]z.

I mean, could you graph this formula/function, for {y, x, w, z}eR?

I could only assumme that you'd map it to 3-space, and 1 time space, making 4 dimensions, or perhaps you could do this in 2D space, with one axis a color spectrum.

Please be aware that there are 100^3 definitions (speaking generally...) for this triadic operator, and I call this the "ultra-operator", or a "wild operator".

Why 100^3?

Well, because:

+/-{0, N, Q, R, T}+/-{0, iN, iQ, iR, iT} gives us 100 possibilitys, where:

N=Integers, Q=Rationals, R=Irrationals, T=Transendentals.

The formula above may even be 8-dimensional if you were to bring in complex numbers, and also, did you consider inverse operations? -Here:

f^-1(a, b)-->(a[b]c)=c, f^-1(b, c)-->(a[b]c)=a, f^-1(a, c)-->(a[b]c)=b.

Remember, also, todays mathematics is tomorrows physics, so perhaps one day these higher operators will have a practical real world application.
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Messages In This Thread
Generalized recursive operators - by Whiteknox - 11/23/2007, 06:42 AM
RE: Generalized recursive operators - by bo198214 - 11/23/2007, 08:41 AM
RE: Generalized recursive operators - by andydude - 11/25/2007, 01:02 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 04:45 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 05:55 AM
RE: Generalized recursive operators - by andydude - 11/29/2007, 06:20 AM
RE: Generalized recursive operators - by andydude - 11/30/2007, 06:12 PM
RE: Generalized recursive operators - by andydude - 11/30/2007, 09:18 PM
RE: Generalized recursive operators - by bo198214 - 03/07/2008, 06:58 PM
RE: Generalized recursive operators - by Ivars - 02/02/2008, 10:11 PM
RE: Generalized recursive operators - by Ivars - 02/03/2008, 10:41 AM
RE: Generalized recursive operators - by andydude - 02/11/2008, 09:47 PM
RE: Generalized recursive operators - by Ivars - 02/14/2008, 06:05 PM
RE: Generalized recursive operators - by GFR - 02/03/2008, 04:12 PM
RE: Generalized recursive operators - by Ivars - 02/03/2008, 08:48 PM
RE: Generalized recursive operators - by GFR - 02/06/2008, 02:44 PM
RE: Generalized recursive operators - by Ivars - 02/06/2008, 02:56 PM
RE: Generalized recursive operators - by Ivars - 02/06/2008, 03:43 PM
RE: Generalized recursive operators - by GFR - 03/10/2008, 09:53 PM
RE: Generalized recursive operators - by GFR - 03/11/2008, 10:24 AM
RE: Generalized recursive operators - by bo198214 - 03/11/2008, 10:53 AM
RE: Generalized recursive operators - by GFR - 03/12/2008, 12:13 AM
RE: Generalized recursive operators - by GFR - 03/13/2008, 06:41 PM
RE: Generalized recursive operators - by Stan - 04/04/2011, 11:52 PM

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