When I started thinking about it I made a number "line" that had an origin (0) with positive in one direction, negative in another, and urgative in a third. Th

When I started thinking about it I made a number "line" that had an origin (0) with positive in one direction, negative in another, and urgative in a third. The reasoning is that a different sign takes you towards the origin, then in the direction of the new sign. The answer to your question is: -1 + +5 = +4 +4 + urg3 = +1 to illustrate some other examples: +5 + urg10 = urg5 -5 + urg10 = urg5 urg5 + -10 = -5 urg5 + +10 = +5 I never actually proved that the arithmetic was consistent, or even useful in any way. Multiplication was much easier to reason about because setting the sign was just the result of a truth table. This is when I figured out the true/false truth tables extended the 3 symbols pretty trivially. I worked through boolean logic and then got bored with it and forgot about it until that time talking to my Calc 3 teacher during office hours.