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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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Robert (Bob) Eldon Taylor

Posts: 101
Registered: 12/3/04
Re: [HM] Dedekind's objection to the Newtonian concept of number.
Posted: Jul 22, 2006 9:46 AM
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Dear Heinz,

Thanks again for the interesting discussion. I am sorry that I am
unable to make my point clear enough for you, but I have learned from
the effort. You are of course correct about Euclid's use of ratios only
in proportion, and the independent use of ratios seems to be an
important development on the route to Newton's definition. However,
even with Newton and beyond, the sense of proportion is always there,
sometimes explicitly, as in the passage from Hamilton I previously cited.

Regards from desiccated Comer, Georgia, USA, which is being teased by
the storm gods,
Bob


Prof. Lueneburg wrote:
>
> Dear Bob and All,
>
> I quit the discussion, because all you are saying is to vague for me to
> follow your way to the complex numbers.
>
> I shall be back as soon as you give a by modern standards mathematically
> sound description of what your are talking about. Then we can go back to
> Dedekind. --- He knew what he was talking about.
>
> By the way, Euclid's or rather Eudoxos' theory of ratios is a theory
> on the quaternary relation of "a and b are in the same ratio as c and d".
> A ratio is never defined in Euclid and, moreover, never used in the text.
> (I know: V such and such. That's why I said "never used in the text".)
>
> 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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