Description:
Mathematical discussions and pursuits.
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Deterministic vs Nondeterministic Turing machines.
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... first of all, is there any generally accepted definition of non- deterministic Turing Machines? At least I have found almost nothing usable, including wiki-articles. So I will state my question in the following form: Is it true, that there exists ‘probabilistic’-TM, which could not be simulated with deterministic-TM at all?... more »
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about CNF converting
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Hi all, did somebody know if is possible to use a non deterministic algorithm in order to convert every boolean propositional formula into an equivalent CNF formula? Thanks a lot Regards
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Dedekind-MacNeille completion
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Let S be an (partially) ordered set. For A subset S, let above A = set of upper bounds of A. below A = set of lower bounds of A. The Dedekind-MacNeille completion of S is M = { below above A | A subset S } If S is a Boolean algebra, then M is a Boolean algebra. In particular, when A subset S, what set B is there for which... more »
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Polyhedron
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I am trying to visualize what looks like a particular polyhedron(?), but I am having a bout of stupidity and cannot figure something simple about it. I am describing the shape, section-wise: Consider the unit circle on the xy-plane. Put vertexes at exp(2*k*Pi/8*i), k \in {0,1,...,7} Rotate the unit circle around the x-axis by Pi/4.... more »
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cheap i jeans hoody
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Farmer Brown's conjecture
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One multiplied by one is two. One instance of one is one. One times one is one. The square root of two is one. In a proper real world counting system, a proper ruler would consist of inch increments whereby each subsequent inch, was longer than the one before it, and if you knew the proper amount to increase each... more »
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A consideration concerning the diagonal argument of G. Cantor
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WM schrieb: ...So what? I have no objections to the notion, that numbers - and ideas in general - depend on physical processes in our brains. The important issue here is, whether these inner-brain images have brain-external counterparts. And I believe, that the physical representation of numbers *at most* exist... more »
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A consideration concerning the diagonal argument of G. Cantor
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Albrecht schrieb: ...No, actually I agree to WM, that ideas depend on physics, i.e. that they're not beyond physics. The important issue here is, whether "things" are outside or inside the brain. And I think, many "things" are only inside a brain, and will vanish, if there is no brain any longer, which is, I believe, a plausible assumption.... more »
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Prove Sup a_n=Inf b_n for (a_n,b_n) sequence of nested intervals
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Let (a_n,b_n) be a sequence of nested open intervals. Assume that intersection of all (a_n, b_n) is empty. Show that Sup a_n=Inf b_n Proof: {a_n} is an increasing sequence bounded above and {b_n} is a decreasing sequence bounded below. We know from previous theorems that since {a_n} and {b_n} are monotonically increasing or decreasing... more »
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