>>13278280Here's an example of some math
Legal words in our math are
M, I, and U
Legal sentences in our math are
Mx
Where x can be any combination of I and U
Examples of legal sentences:
MIIIUU
MIU
MIUIUIU
Examples of illegal sentences
IUMUI
MURU
UWUM
You can travel in our math using the following rules:
(a) You can turn Mx into Mxx
example: MIU -> MIUIU
(b) You can turn MxIIIy into Mxy
example: MIUUIIIU -> MIUUU
(c) You can turn MxU into MxI
example: MIUIU -> MIUII
(d) You can turn MxI into MxU
example: MIUI -> MIUU
Here's an example of a derivation of MUU from MU:
(by c) MU -> MI
(by a) MI -> MII
(by a) MII -> MIIII
(by d) MIIII -> MIIIU
(by a) MIIIU -> MIIIUIIIU
(by b) MIIIUIIIU -> MUIIIU
(by b) MUIIIU -> MUU
Except in the math you learn in school, they encode in the rules the properties of useful things, like numbers and logic.
Here's an example of some properties that are encoded in widely used systems of math:
https://www.varsitytutors.com/hotmath/hotmath_help/topics/properties-of-equalityhttp://www-groups.mcs.st-andrews.ac.uk/~edmund/lnotes/node4.html 
