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.