Dialogue on n-Color Arithmetic (4)

Part 4:
Notes on 2-Number Arithmetic

Si Emo had a patience to wait to listen to Si Nessa's adventure with the Many-Colored Numbers. But to his surprise Ki Algo told him that not all arithmetic is about numbers
Si Emo:  Any other arithmetic?
Ki Algo: The mathematical modulo 2 arithmetic can be rewritten as qualitative verbal arithmetic. By replacing A with Even Number and B with Odd Number, we get the following addition table

+	Even Number	Odd Number
Even Number	Even Number	Odd Number
Odd Number	Odd Number	Even Number

and the multiplication table

.	Even Number	Odd Number
Even Number	Even Number	Even Number
Odd Number	Even Number	Odd Number

Si Emo: Oh, no. I have never thought about that.

Logical Arithmetic

Ki Algo: The other system is logical arithmetic that we get if we replace A with False, B with True and the operations + and * with XOR and AND respectively to get the addition table

XOR	False Statement	True Statement
False Statement	False Statement	True Statement
True Statement	True Statement	False Statement

and the multiplication table

AND	False Statement	True Statement
False Statement	False Statement	False Statement
True Statement	False Statement	True Statement

Si Emo:  My goodness. I thought arithmetic is just for numbers.

Ki Algo: Yes arithmetic is not about numbers. Polynomial can also has arithmetic. It's arithmetic is a ring, but sometimes the finite degree polynomials will have field structure arithmetic like real numbers. But, in general, the finite degree polynomial forms a ring: the ring of polyplex numbers.

Si Emo: Will you teach me the polyplex arithmetic?

Ki Algo: OK. It will help you to understand many-colored numbers. Wait till the next session of the dialogue.