09/16/2021, 11:34 PM

another idea are my " xyz numbers ".

They are also a commutative 4d type of number.

x*x = y*y = -1

x*y = y*x = 1.

x*z= z*x = y

y*z = z*y = - x

z*z = - 1 + x + y

notice many properties are not present ; not associative , nilpotent , no unique inverses etc

For instance

(x+y)^2 = 0

but x+y is not 0.

-x*x = y*x = 1.

but -x is not y.

still investigating.

what do you think ?

regards

tommy1729

They are also a commutative 4d type of number.

x*x = y*y = -1

x*y = y*x = 1.

x*z= z*x = y

y*z = z*y = - x

z*z = - 1 + x + y

notice many properties are not present ; not associative , nilpotent , no unique inverses etc

For instance

(x+y)^2 = 0

but x+y is not 0.

-x*x = y*x = 1.

but -x is not y.

still investigating.

what do you think ?

regards

tommy1729