Hi Doug,
most likely this is my last post on this subject:
You have defined at least 5 slots since you defined e_0^2 =1
Do you not notice eq. 4 violates:
The first term of eq.4 is a pure number without a factor of e_0 and violates "that every term has a basis vector, no exceptions"...
Hello Doug,
The problem is equation 3 can not mitigate the fact that you introduced basis elements that square to plus or minus “1” . (e_0)^2= 1 So there you have it, “one”, in all its naked glory. Either the number one is a legitimate element, or our “quaternions” are not closed under the...
Hi Doug,
Mathemaica is a wonderful tool but I sometimes think too much of it can be the crutch that cripples so I’m going to use good old fashioned algebra. You have stated (e_0)^2=1, correct? Well then (1+ e_0)(1- e_0)=0 since we have 1^2 – e_0 + e_0 – (e_0)^2 =0. That is to say 1+e_0 and...
Hello Doug,
The algebra you describe below is not the quaternions, that is to say it is not isomorphic to the quaternions. What you have is not a division algebra. For example: what is 1/(1+e_0) ?
1+e_0 has no inverse.