Comment on What are the 'real numbers', really?parentComments−claudius12yBy your definition of <, 0 < i and i^2 < 0, however, the OP requires that 0 < p AND 0 < q => 0 < p * q, which is not fulfilled by your < for p = i = q.
Comments
By your definition of <, 0 < i and i^2 < 0, however, the OP requires that 0 < p AND 0 < q => 0 < p * q, which is not fulfilled by your < for p = i = q.