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1d
revised Is it allowed to define a number system where a number has more than 1 representation?
second example
1d
comment define the “optimal” automatic theorem prover
I don't think that any extant theorem provers work like that. As I said earlier, HR is the only system I know that works along those lines -- but it's not a theorem prover, I think it uses Otter (and MACE?) to do that.
1d
comment define the “optimal” automatic theorem prover
See pages.cs.miami.edu/~tptp/CASC/J7/SystemDescriptions.html for descriptions of the strategies employed by some of the leading ATP systems.
1d
comment define the “optimal” automatic theorem prover
The state of the art is much smarter than merely randomly exploring a tree!
1d
comment define the “optimal” automatic theorem prover
But we don't have any automated provers which understand concepts in that sense. They're much smarter than the random prover but not at all insightful.
1d
comment define the “optimal” automatic theorem prover
Most theorem provers are of type (1), and usually they are quite limited -- in a practical sense you ask them to prove small steps toward a theorem, but you still have to map out the path. The only example I know of for (2) is Colton's HR.
1d
comment define the “optimal” automatic theorem prover
I don't think that (2) is equivalent to (1). A theorem prover might have a thousand or even a million sub-results along the way to prove a certain theorem, but not know which are interesting and which are boring.
2d
answered Is it allowed to define a number system where a number has more than 1 representation?
2d
comment Union of a null set and a non-measurable set
@Bey: Yes, that is precisely my reason for asking!
2d
accepted Union of a null set and a non-measurable set
2d
asked Union of a null set and a non-measurable set
2d
comment Where $ax + b$ prime infinitely often, is $ax + b - 2$ semiprime at least once?
@RobertGross: Right, to say that you'd need Dickson's conjecture, as I mentioned. It doesn't follow from Dirichlet alone.
Jun
18
answered Is this a valid equivalent expression of the twin prime conjecture?
Jun
18
answered Estimating total number of twin primes
Jun
17
answered How big is the chance that a arbitrary man is taller than a arbitrary woman?
Jun
17
comment Where $ax + b$ prime infinitely often, is $ax + b - 2$ semiprime at least once?
@RobertGross: Yes, why don;t you post that specific case as a new question? If $a$ is a product of primes (not necessarily twins) then there's at least a chance it will work.
Jun
16
answered When $\pi(x) \leqslant 0.4x +1$?
Jun
16
comment Where $ax + b$ prime infinitely often, is $ax + b - 2$ semiprime at least once?
@RobertGross: OK, so choose $a=315,\ b = 107$.
Jun
16
awarded  Nice Answer
Jun
16
comment Where $ax + b$ prime infinitely often, is $ax + b - 2$ semiprime at least once?
@RobertGross: Clearly that's not possible, given my counterexample of $a=105,\ b=2.$