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Topic: [HM] Dedekind's objection to the Newtonian concept of number.
Replies: 23   Last Post: Aug 2, 2006 12:39 AM

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Heinz Lueneburg

Posts: 226
Registered: 12/3/04
Re: [HM] Dedekind's objection to the Newtonian concept of number.
Posted: May 23, 2006 8:53 AM
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On Fri, 19 May 2006, Robert Eldon Taylor wrote:

>
> Dear Heinz,
>
> Well I think I will leave it up to you to parse the distinctions between
> "not founded" and "invalid", In any case these foundation issues are
> something you brought up and, in my view, irrelevant. One thing is
> clear, though you seem unwilling to admit it, Dedekind was wrong to say
> that the then accepted understanding of number as a ratio could not be
> extended to include complex numbers. Whether a better way is a matter
> of taste, not history.
>

Dear Bob,

As long as you do not see the difference between "not founded" and
"invalid", you will not have understood Dedekind's remark your are
critizising. "Foundation" is Dedekind's point, not mine.

I do not see how Euclid's book V can be extended to include also the
complex numbers in its theory of proportions. What you are saying in your
postings is to vague for me as a mathematician to point to the place
where the reals come in. I am sure they come in at a crucial point whilest
constructing the complex numbers.

All the best, Heinz Lueneburg



Date Subject Author
5/26/05
Read [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/3/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/8/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/16/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/17/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/19/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/23/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/27/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/28/06
Read [HM] Periodicity
Samuel S. Kutler
5/29/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Samuel S. Kutler
6/26/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/29/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
6/21/06
Read [HM] An Arbitrary Quadrilateral
Samuel S. Kutler
6/22/06
Read Re: [HM] An Arbitrary Quadrilateral
Joseph Malkevitch
6/22/06
Read Re: [HM] An Arbitrary Quadrilateral
Emmanuel Cardona
6/25/06
Read [HM] Geometric Representation of Complex Numbers
Samuel S. Kutler
6/26/06
Read Re: [HM] Geometric Representation of Complex Numbers
Luis Puig
6/26/06
Read Re: [HM] Geometric Representation of Complex Numbers
Ken.Pledger@vuw.ac.nz
6/27/06
Read Re: [HM] Geometric Representation of Complex Numbers
Sanford L. Segal
8/2/06
Read Re: [HM] Geometric Representation of Complex Numbers
Romulo Lins
6/26/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
7/19/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
7/22/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
7/11/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor

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