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tech / sci.math / A deficiency of the Dedkind cuts

SubjectAuthor
* A deficiency of the Dedkind cutsredsto...@163.com
+- Re: A deficiency of the Dedkind cutsWho's Identity Is A Very Big Secret
+- Re: A deficiency of the Dedkind cutsWho's Identity Is A Very Big Secret
+- Re: A deficiency of the Dedkind cutsDan Christensen
`- Re: A deficiency of the Dedkind cutsTimothy Golden

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A deficiency of the Dedkind cuts

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Subject: A deficiency of the Dedkind cuts
From: redstone...@163.com (redsto...@163.com)
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 by: redsto...@163.com - Fri, 6 Jan 2023 09:19 UTC

I posted it in my blog
https://redstoneleo.blogspot.com/2023/01/one-deficiency-of-dedkind-cuts.html
Welcome to discuss about it.

Re: A deficiency of the Dedkind cuts

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Subject: Re: A deficiency of the Dedkind cuts
From: angel000...@icloud.com (Who's Identity Is A Very Big Secret)
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 by: Who's Identity - Fri, 6 Jan 2023 10:39 UTC

Math gets so boring, if You get to know, that No=Yes.

On Friday, January 6, 2023 at 11:19:26 AM UTC+2, redsto...@163.com wrote:
> I posted it in my blog
> https://redstoneleo.blogspot.com/2023/01/one-deficiency-of-dedkind-cuts.html
> Welcome to discuss about it.

Re: A deficiency of the Dedkind cuts

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Subject: Re: A deficiency of the Dedkind cuts
From: angel000...@icloud.com (Who's Identity Is A Very Big Secret)
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 by: Who's Identity - Fri, 6 Jan 2023 10:45 UTC

Math gets so boring, when You get to know, that No is Yes.

On Friday, January 6, 2023 at 11:19:26 AM UTC+2, redsto...@163.com wrote:
> I posted it in my blog
> https://redstoneleo.blogspot.com/2023/01/one-deficiency-of-dedkind-cuts.html
> Welcome to discuss about it.

Re: A deficiency of the Dedkind cuts

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Subject: Re: A deficiency of the Dedkind cuts
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Fri, 6 Jan 2023 16:34 UTC

On Friday, January 6, 2023 at 4:19:26 AM UTC-5, redsto...@163.com wrote:
> I posted it in my blog
> https://redstoneleo.blogspot.com/2023/01/one-deficiency-of-dedkind-cuts.html
> Welcome to discuss about it.

Not sure, but it's probably a standard theorem of real analysis. You might have more luck at https://math.stackexchange.com/questions

You should post the text, not just the link there. Their interface supports Latex

Dan

Re: A deficiency of the Dedkind cuts

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Subject: Re: A deficiency of the Dedkind cuts
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Fri, 6 Jan 2023 17:38 UTC

On Friday, January 6, 2023 at 4:19:26 AM UTC-5, redsto...@163.com wrote:
> I posted it in my blog
> https://redstoneleo.blogspot.com/2023/01/one-deficiency-of-dedkind-cuts.html
> Welcome to discuss about it.

Don't you really have a double cut there? Pretty sure the theme is a singular cut.
I still think that attacks on it are of interest. Digit chasing is all that I see.
The fact that operators and values are distinct concepts means that the mixing of the two as if they are pure values is a fraud.
This implies then that even the rational value is a fraud. Every rational value is composed of two values and an operator. Further, the operator is not even fundamental; it is an inverse operator; typically lacking in computability. Closure is completely ignored in the construction of the rational value. By this means much of real analysis collapses. Heading back to the digits we have workable values via the decimal point, or the radix point, but it's interpretation on its own merit is as a modifier to the natural value; it proposes a secondary form of unity. Computing the sqrt(2) is a matter of chasing digits, and I don't see how Dedekind's cut is any different. To truly run through the gauntlet is to chase down the digits. The practical rate of your epsilon is one tenth of what it was. Coding this we simply take the product of a value x with itself and compare it to two. As it is off we make corrections, then refine those corrections, and pretty quickly we are down chasing the digits. By this method we are relying only upon the product to make the answer materialize, and this is far more fundamental than division. Hardware division, even of integers yielding integers, is problematic.

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