Description:
Logic -- math, philosophy & computational aspects.
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Differential
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I think it's funny that many will readily accept some least infinite, but not some greatest infinitesimal: the differential. I also think it's sad. That's OK, though, Fraenkel says we'll recover, to Cantor's bacilli: the infinitesimals. It's funny how differentials are defined in terms of generally... more »
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jumps in the complexity of ordinals
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Starting with the smallest infinite ordinal omega, we can look for points where there's a jump in complexity. Omega + 1 is a a successor ordinal; so it's ordinary. Same for omega + n, n<omega. Next, omega+omega seems no more complex than omega. So, after a while, we get to omega^2 . It's a limit ordinal, so maybe... more »
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Real Discontinuity in Cantor Diagonal
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with regard to lists of real numbers: (My problem is NOT with the diagonal argument itself per se, but rather with one of its underlying assumptions) How does one prove that the statement: "diagonalization is only applicable to lists of any finite size " is false.? It obviously IS true that FINITE lists of reals can be diagonalized,... more »
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Darkmatter is Hypermatter.By Aiya-Oba
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Darkmatter is pair of the remote Space, to which every unit of the visible matter is equator.-Aiya-Oba (Poet/Philosopher). Thus, (m/m^2 + 2) x m^2 = 2(m^2) + m Where m, is visible matter, and 2(m^2), is hypermatter (remote Space) or darkmatter, and m, can be any natural number. Such that, m = 10... more »
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Interpretation problem
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Hey guys, Any help you could provide with this is greatly appreciated. F = (AX)(p(s(X)) -> p(X)) and G = (EX)p(X) Where A = for all and E = exists Use as domain the set N = {0,1,2,...} of natural numbers. Having trouble with the following: 1. Describe an interpretation where F ^ ¬G is true or argue that such an... more »
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Subcardinality
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Hi all, Actually one can define subcardinalities like w-1, w-2 ,..., w/2 , nth root of w, etc.... Although a lot say that this is not the traditional approach and doubt it but it can be done. I will give here an informal method to how that can be done. It can be done using Gap-fill methodology. Subcardinality is concerned with subsets of Omega.... more »
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