This chapter transitions from the foundational topics of the previoustwo chapters, to more “working” mathematics. Thischapter builds up intuitions about some simple algebraic concepts– groups, rings, and fields. Some diagrams of“inconsistent vectors” are played with. The discussionis organized around how to deal with an open problem in inconsistentmathematics from Dunn and Mortensen, of how to allow some nontrivialinconsistency in fields. The idea of using relative unit elements ingroup cancellation – more than one “zero”number – is introduced as a possible solution, and its basicrules are developed.