I always like stuff like bicomplex numbers , hypercomplex numbers etc
And some of you here do to.
So I thought I share my " tommy quaternion " with you.
Do not confuse with the normal quaternion or hyperbolic quaternion.
The nonreal units are \( A,B,C \)
And the rules for the units are :
\( A*B=B*A=C,A*C=C*A=-B \)
\( B*C=C*B=A \)
\( A*A=B*B=-1 \)
\( C*C=1 \)
The distributive property holds.
And clearly this is a commutative number system.
But not associative.
A pair of zero divisors are \( (A+B)(A-B)=A^2 - B^2 = -1 - -1 = 0 \)
The word " anti-associative " comes to mind.
Im considering doing tetration with them.
Feel free to comment.
Regards
tommy1729
Tom Marcel Raes
And some of you here do to.
So I thought I share my " tommy quaternion " with you.
Do not confuse with the normal quaternion or hyperbolic quaternion.
The nonreal units are \( A,B,C \)
And the rules for the units are :
\( A*B=B*A=C,A*C=C*A=-B \)
\( B*C=C*B=A \)
\( A*A=B*B=-1 \)
\( C*C=1 \)
The distributive property holds.
And clearly this is a commutative number system.
But not associative.
A pair of zero divisors are \( (A+B)(A-B)=A^2 - B^2 = -1 - -1 = 0 \)
The word " anti-associative " comes to mind.
Im considering doing tetration with them.
Feel free to comment.
Regards
tommy1729
Tom Marcel Raes