Description:
Logic -- math, philosophy & computational aspects.
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Class Theory /\
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Hi all, Theory /\ is the set of all sentences entailed by (using FOL with identity and the primitives "in" and "V" were V is a constant) the following non logical axioms: Definition: x is a set iff x in V Definition: x is a class iff [ x in V or ~ x in V ] So we have: for all x : x is a class.... more »
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Difference between informal and formal proofs?
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What's the difference b/w a formal and an informal proof, in mathematics? I have an informal proof that sqrt(2) is irrational: 1. Assume sqrt(2)=x/y, where x and y are nonzero integers and relatively prime 2. y*sqrt(2)=x 3. 2y^2=x^2 4. x=2z, since x^2 is even by this, since it is able to be divided by... more »
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Started to puzzle with PA again. an i am wondering In Pa Prov is true iff the formula x is provable Ax [Prov(x) -> Prov(Prov(x))] and ~Ax[Prov(x) <-> Prov(Prov(x))] Therefore Ex[ Prov(Prov(x)) & ~Prov(x)] what is an example of formula x? I just don't understand Prov(Prov(x)) what is the difference between Prov(Prov(x)) and Prov(x)?... more »
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