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Re: Applications of Wmath
Posted:
Aug 21, 2014 4:32 AM


On Wednesday, August 20, 2014 8:02:27 PM UTC+10, Jürgen R. wrote: > I think we can all agree that no progress has been made in > > clarifying the basis of Mueckenheim's criticism of > > traditional math (Tmath as opposed to Wmath), despite years > > of discussion. > > > > Let us, for the moment, accept the basic principles of Wmath: > > > > 1.A mathematician doesn't need silly, arbitrary axioms, > > definitions and tedious technical proofs. Common sense, a > > "sober mind", is quite enough. > > > > 2.Mathematics makes sense only to the extent that it models > > the real world, i.e. physics. > > > > 3.Something goes drastically wrong when logic derived from > > finite objects is applied to infinite collections. > > > > 4.Wmath seeks to return (in a manner not clearly > > articulated) to a discrete, semifinitary form of mathematics. > > > > So rather than continuing the futile discussion about the > > foundations of Wmath, let us ask Mueckenheim to demonstrate > > how it is applied to a basic problem in mathematical physics: > > > > Consider the equation > > > > (P(x)y')'  Q(x)y = rR(x)y. > > > > An eigenvalue problem that is ubiquitous in physics. > > > > P, Q and R are realvalued functions of the real variable x, > > a < x < b. b may be infty. P > 0, R > 0. P in C^1[a,b], Q > > and R in C^0[a,b]; r a constant to be determined. y(x) > > satisfies some reasonable boundary conditions at a and b. > > Try for starters y(a) = y(b) = 0. > > > > There are lots of properties of the solutions of such > > equations derivable in Tmath; e.g. that the eigenvalues are > > real, that the eigenfunctions are orthogonal and span the > > infinitedimensional Hilbert space L^2[a,b], oscillation > > properties of the solutions etc. etc. > > > > What can be said about such an equation in Wmath, where > > there are gaps in the real axis, no uncoutable collections,
Q1/ What Engineering problem does this equation solve buy using 'uncountable collections' ?
Q2/ What Engineering problem does this equation solve that cannot be framed in a finite set theory ?
For Clarification, in calculus there need not be an oo symbol by itself, >oo is sufficient.
Q3/ What concrete proof do you have EXIST(SET) SET>Inf ?
Q4/ What guarantee do you have that given a countable enumeration of subsets of N, that Cantor's Missing Set...
1eC <> 1~eS1 AND 2eC <> 2~eS2 AND 3eC <> 3~eS3 AND 4eC <> 4~eS4 AND ...
must exist and that
C = { n  n~eSn }
isn't just Real Jargon.
How many Free Variables are in your proof
EXIST(C) > EXIST(S) CeS & S>Inf
Can you parse the following English paragraph.
"If the 1st Subset in the Set Of All Subsets has a 1 then C doesn't AND if the 1st Subset in the Set Of All Subsets doesn't have a 1 then C does AND If the 2nd Subset in the Set Of All Subsets has a 2 then C doesn't AND if the 2nd Subset in the Set Of All Subsets doesn't have a 2 then C does AND SO ON...
Can you write a formula for the above Paragraph?
What would you call it?
Have you read www.MUD.com/news Today ?



