mijcar Quantum Meta-Fields What is a Quantum Meta-Field? Quantum Meta-Field over the real numbers: A set R* is a Quantum Meta-Field over the real numbers iff - Any member M of R* is a set that meets the following conditions: - - M is a subset of the real numbers and for any m in M, there is a "next" m* (that is, there is no member of M that is between m and m*). Postulate: R* is well-defined and of order c. Theorems that are obvious: - Any finite subset of the real numbers is a member of R*. - Any subset of the integers is a member of R*. - For any given real e>0, there is a set E that is a member of M and which has the properties such that any real number is within e of a member of E. - For any given real e>0 and any finite subset S of the real numbers, there is a finite member F of M such that for any member s of S, there is a member of F that is within e of s. - For any given e>0 and any finite math problem (i.e., finite numbers and finite operations) there are an infinite number of finite subsets P of M such that the numbers of the problem are members of P and that the solution if within e of some member of P. - For any finite real world system with a finite number of computations, there is an infinite number of finite members of M that will solve that problem within any desired degree of accuracy. Questions: Can one set e>= 0? Yes, in most cases (I say that only to be cautious -- I have not yet conceived of any situation where the answer is "no"). However, there is no real world situation in which e would equal 0.
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