Mu System

[anduril66]

Did anyone read Godel, Escher, Bach?
I thought I found an answer to the MU formal system, but there isn't supposed to be any.


Rules:
1. If xI is a theorem, so is xIU.
2. If Mx is a theorem so is Mxx.
3. Ifn any theorem III can be replaced by U.
4. UU can be dropped from any theorem.

Axiom: MI
Goal: To get MIU

What I did:
Use Rule 2 to double I 32 times to get M followed by 42957296 (or 8589934592, etc). 2 raised 32 is a multiple of 3.
Use Rule 3 to rplace the Is with 1431655765 Us.
Use Rule 4 to drop all Us but one, leaving MU.

Do you see any errors?

Thanks.

Do you recommend another place to ask this?

[DarkerLine]

2^32 is not a multiple of 3, it just appears this way if you type in 2^32/3 onto the calc because it only shows 10 digits.

[62 52 53 53]

Given: MI
Proove: MIU
statements.......................reasons
1) MI...............................1)G
2) MII..............................1)Mx=Mxx
3) MIIII............................1)Mx=Mxx
4) MIU.........(Q.E.D)..........1)III=U

Moral of the story: either the problem has something to it that wasn't clearly stated, or there was a typo, or everyone else to try to solve it is stupid.
I vote for the second, since: "Use Rule 4 to drop all Us but one, leaving MU."

[anduril66]

Yeah, you're right about the 2 to the 32nd not being divisible by 3.

Sorry for the mistake, but you're given MIU and have to prove MU.