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Topic: Re: Number line
Replies: 1   Last Post: Feb 23, 2009 1:09 PM

 Messages: [ Previous | Next ]
 James A. Landau Posts: 17 Registered: 10/15/08
Re: Number line
Posted: Feb 23, 2009 12:58 PM

>--- Samuel.Kutler@sjca.edu wrote:
>
>From: "Kutler, Samuel" <Samuel.Kutler@sjca.edu>
>To: <JJJRLandau@netscape.com>, <MATH-HISTORY-LIST@ENTERPRISE.MAA.ORG>
>Subject: RE: Number line
>Date: Mon, 23 Feb 2009 07:00:42 -0500
>
>The number line, in my opinion, is our chief image
>in mathematics to our so called number systems,
>and did it have to wait until Dedekind to be such?
>Insofar as Descartes is our father,
>he sets the stage for it,
>but it is unlike him to state it clearly.
>Of course, Gauss and 2 others
>almost simultaneously
>introduced us to the complex PLANE.

Dedekind wrote (emphasis mine):

<quote>
This analogy between rational numbers and the points of a straight line, AS IS WELL KNOWN, becomes a real correspondence when we select upon the straight line a definite origin or zero-point o and a definite unit of length for the measurement of segments.
</quote>

So Dedekind appears to be saying that the concept of the number line was well known in 1872.

Whether anyone before 1872 made signifcant use of the number line concept, I don't know.

One idea for research: who came up with the concept of open and closed intervals (and the convention that the real number line is both open and closed)? That concept appears, to me, to be closely connected with the idea of the number line.

- James A. Landau

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Date Subject Author
2/23/09 James A. Landau
2/23/09 Fernando Q. Gouvea