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tech / sci.math / Re: Dedekind was a crank.

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* Re: Dedekind was a crank.Timothy Golden
`- Re: Dedekind was a crank.Meritocracy

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Re: Dedekind was a crank.

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Subject: Re: Dedekind was a crank.
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Mon, 17 May 2021 12:40 UTC

On Tuesday, May 11, 2021 at 8:13:42 AM UTC-4, Eram semper recta wrote:
> On Monday, 10 May 2021 at 18:39:57 UTC-4, timba...@gmail.com wrote:
>
> > This is Dedekinds first usage of 'cut'. He then goes on to the upper bound and describes a value oscillating and settling to arbitrarily small error. This is no different that a kid computing the square root of two by guessing the next digit and refining via computation. There is room for criticism, but the result I find to be in line with my own thinking on the puzzle.. It's called arbitrary precision. Close enough is good enough.
> Er, no. "Close enough is not good enough". A measure is either a measure or it is not.
>
> Dedekind (like you) knew NOTHING about measure. He only knew that he and all his peers were clueless. Chuckle.

"Moreover, a sufficiently small definite segment is taken as a unit segment, and from
this by continued bisection and semi-rotation a system of points is constructed of the
kind that to each point of this system a definite number a corresponds, which is rational
and has as denominator some power of 2. By setting up a law concerning this correspondence, the points of the above system are so arranged that the above laws concerning
mutually tangent circles are valid. It is now shown that the points corresponding to the
numbers 1/2, 1/4, 1/8, . . . converge toward the point 0. This result is generalized step by step
until it is finally shown that every series of points of our system converges, so soon as
the corresponding series of numbers converges."
- https://math.berkeley.edu/~wodzicki/160/Hilbert.pdf

Is this really any better? Or is it the same analysis?

Re: Dedekind was a crank.

<s7usfk$t4r$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=59342&group=sci.math#59342

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From: inva...@invalid.com (Meritocracy)
Newsgroups: sci.math
Subject: Re: Dedekind was a crank.
Date: Mon, 17 May 2021 17:59:02 -0500
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 by: Meritocracy - Mon, 17 May 2021 22:59 UTC

On 5/17/2021 7:40 AM, Timothy Golden wrote:
> On Tuesday, May 11, 2021 at 8:13:42 AM UTC-4, Eram semper recta wrote:
>> On Monday, 10 May 2021 at 18:39:57 UTC-4, timba...@gmail.com wrote:
>>
>>> This is Dedekinds first usage of 'cut'. He then goes on to the upper bound and describes a value oscillating and settling to arbitrarily small error. This is no different that a kid computing the square root of two by guessing the next digit and refining via computation. There is room for criticism, but the result I find to be in line with my own thinking on the puzzle. It's called arbitrary precision. Close enough is good enough.
>> Er, no. "Close enough is not good enough". A measure is either a measure or it is not.
>>
>> Dedekind (like you) knew NOTHING about measure. He only knew that he and all his peers were clueless. Chuckle.
>
> "Moreover, a sufficiently small definite segment is taken as a unit segment, and from
> this by continued bisection and semi-rotation a system of points is constructed of the
> kind that to each point of this system a definite number a corresponds, which is rational
> and has as denominator some power of 2. By setting up a law concerning this correspondence, the points of the above system are so arranged that the above laws concerning
> mutually tangent circles are valid. It is now shown that the points corresponding to the
> numbers 1/2, 1/4, 1/8, . . . converge toward the point 0. This result is generalized step by step
> until it is finally shown that every series of points of our system converges, so soon as
> the corresponding series of numbers converges."
> - https://math.berkeley.edu/~wodzicki/160/Hilbert.pdf
>
> Is this really any better? Or is it the same analysis?
>

(Mr Rectum up-chuckles on his own-self, again)

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