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.
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.