ex-xian

So you've absorbed and mastered all the subjects listed in this index?

Lemur

No, it was deliberately stupid.

Just making it clear that I was using that as an example. I would never myself of course actually try to make that "proof" to any serious math people.

Doron Shadmi

Lemur,

A one rotation of the Archimedean Spiral is exactly 1/3 of the circle’s area if and only if it is a non-composed element, and so is the circle.

If the Archimedean Spiral or the circle are composed elements, then the Archimedean Spiral is not exactly 1/3 of the circle’s area.

One of these non accurate states is 0.33333... < 1/3.

Wall, that's the whole point of my argument.

A model that is based on "infinitely many ...", is totally different from a model of "a non-composed element".

0.3333... is based on "infinitely many different scale levels" where 1/3 is based on "a non-composed element".

If you understand this post, then please re-read very carefully my first post.

Thank you.

Doron Shadmi

A productive dialogue with me is based on notions, not on names, notations, or any technical manipulations with them.

If you warship names, notations and technical manipulations with them and call it actual Mathematics, then there is no and there will not be any dialogue between us.

Since this is a philosophy forum, it maybe help you to make some switch in your mind and open it to the new notions of my work, instead of being stacked time after time on the surface level of names, notations, and technical manipulations.

ex-xian

Congratulations on again missing the point and avoiding the issue.

I asked you what fundamental concepts of Actual Mathematics that you incorporate. You cited "epsilon" as a fundamental concept and you even have "epsilon" as one of you "key words" in your "abstract." This shows terrible ignorance of how analysis is done or what use delta-epsilon proofs actually have.

You brought the word up, then, in what I quoted above, you attack me for calling you on it. I don't worship the technical language of mathematics--but I do call Bullshit when I see people like you misusing it.

Doron Shadmi

Congratulations on again NOT reading my work.

Indeed this is all you can see, but it is in your yard because you are the one who permanently refuses to read my original and better interpretation about the epsilon/delta definitions, because you afraid to change your cozy common point of view.

[edited]

There is a fundamental conceptual mistake behind the standard delta-epsilon understanding.

My better understending of these concepts can be found in: http://www.geocities.com/complementa...ointModels.pdf

Kalkin

This looks like it has degerated into totally unproductive personal bickering. I'm sending it to ~E~.

Lemur

I don't. Please define "non-composed". You have used that phrase in a lot of your definitions but I don't know what it means. Apparently understanding it is necessary to understand your proof that .3333<1/3. If it's a term that must necessarily deny rigorous definition (like "point" in Euclidean geometry) then please give me a good heuristic understanding of it.

Doron Shadmi

Lemur, here is again a part of my first post:


A non-composed element is an element which is not composed of sub-elements.

Lemur

What's an element?

What does it mean to be composed? For example, how exactly would I ascertain the truth or falsity of the statement "X is a composed element"?

Without the answer to those questions I have no idea how to evaluate the following statement:

or this statement

You state this as if this is obvious when in fact it is not (assuming I understand your terminology). If what follows in the OP is a proof of this statement then I do not understand your proof.