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*** GEORGE'S SET THEORY ***
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Graham Cooper
Oct 5, 2012, 8:54:06 PM10/5/12
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GEORGE'S SET THEORY!
*****************************
GEORGE'S RELATION ALGEBRA!
aRb
GEORGE'S INFERENCE RULES!
P -> P
~(X -> ~X)
GEORGE'S SET AXIOMS!
1. Extensionality:
AxAy [Az (zex <-> zey) -> xey]
2. Regularity:
Ax [Ea (aex) <-> Ey (yex & ~Ez (zey & zex))]
3. Specification Schema:
AzAw_1...w_nEyAx [xey <-> (xez & phi)]
4. Pairing:
AxAyEz (xez & yez)
5. Union:
AfEaAyAx [(xey & yef) -> xea]
6. Replacement Schema:
AaAw_1...w_n [Ax (xea -> E!y phi) -> EbAx (xea -> Ey (yeb & phi)]
7. Infinity:
Ex [0ex & Ay (yex -> S(y)ex)]
8. Powerset:
AxEyAz [z subset x -> zey]
9. Wellordering:
AxEr (r wellorders x)
GEORGE'S VALIDATED PROOFS!
THEOREM 1 = ..
THEOREM 2 = ..
THEOREM 3 = !E(R) XeR <-> !(XeX) *TADAAAA*
...
JUST ADD 3 WORDS TO MEAN THE SAME TERM
FOR EVERY TERM THAT YOU USE
SO YOU CAN ALWAYS SWAP TERMS
EG. WHEN ASKED ...
"WHERE'S THE FRICKIN' THEOREMS???"
Herc
*****************************
GEORGE'S RELATION ALGEBRA!
aRb
GEORGE'S INFERENCE RULES!
P -> P
~(X -> ~X)
GEORGE'S SET AXIOMS!
1. Extensionality:
AxAy [Az (zex <-> zey) -> xey]
2. Regularity:
Ax [Ea (aex) <-> Ey (yex & ~Ez (zey & zex))]
3. Specification Schema:
AzAw_1...w_nEyAx [xey <-> (xez & phi)]
4. Pairing:
AxAyEz (xez & yez)
5. Union:
AfEaAyAx [(xey & yef) -> xea]
6. Replacement Schema:
AaAw_1...w_n [Ax (xea -> E!y phi) -> EbAx (xea -> Ey (yeb & phi)]
7. Infinity:
Ex [0ex & Ay (yex -> S(y)ex)]
8. Powerset:
AxEyAz [z subset x -> zey]
9. Wellordering:
AxEr (r wellorders x)
GEORGE'S VALIDATED PROOFS!
THEOREM 1 = ..
THEOREM 2 = ..
THEOREM 3 = !E(R) XeR <-> !(XeX) *TADAAAA*
...
JUST ADD 3 WORDS TO MEAN THE SAME TERM
FOR EVERY TERM THAT YOU USE
SO YOU CAN ALWAYS SWAP TERMS
EG. WHEN ASKED ...
"WHERE'S THE FRICKIN' THEOREMS???"
Herc
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