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Topic: Applications of Wmath
Replies: 8   Last Post: Aug 21, 2014 5:02 AM

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Graham Cooper

Posts: 4,295
Registered: 5/20/10
Re: Applications of Wmath
Posted: Aug 21, 2014 4:32 AM
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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, semi-finitary 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 real-valued 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
>
> infinite-dimensional 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?













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