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Topic: Re: number line
Replies: 0

 Kutler, Samuel Posts: 5 Registered: 4/2/07
Re: number line
Posted: Feb 27, 2009 6:32 AM

I myself do not think that irrational numbers existence, l think we invented them.

-----Original Message-----
From: James A. Landau <JJJRLandau@netscape.com> [mailto:JJJRLandau@netscape.com]
Sent: Wed 2/25/2009 9:24 AM
To: MATH-HISTORY-LIST@ENTERPRISE.MAA.ORG
Subject: Re: number line

(my apologies if this post appears twice; I couldn't tell if it were received the first time)

I was not thinking of the "arrow of time"; I was just trying to think of
early math techniques that approached (asymptotically?) the concept of
"number line". Hipparchus and his Stereographic Projection (not
"Stereographic Transformation" as I incorrectly wrote) came to mind for
the irrelevant reason that my daughter once used it to solve a homework
problem ("show a one-to-one correspondence between the interval (0,1)
and the real number line").

As you have pointed out, the Egyptians had an elaborate system of
rational numbers. Did they know of the existence of irrational numbers?
Or did the Pythagoreans make that discovery? I honestly don't know.

- James A. Landau

--- discussions@MATHFORUM.ORG wrote:

From: Milo Gardner <discussions@MATHFORUM.ORG>
To: MATH-HISTORY-LIST@ENTERPRISE.MAA.ORG
Subject: Re: Number line
Date: Mon, 23 Feb 2009 09:02:37 EST

James,

Thank you for discussing the 'arrow of time'. It can be offered as a
central mathematical arithmetic metaphor of mathematics. Please continue
with the discussion if you so desire.

Historically, well before Dedekind, and modern views of theoretical
arithmetic foundations, the Chinese proved the relevance of the circle
as a foundation of the Chinese Remainder Theorem, and the eastern form
of theoretical arithmetic.

The Greeks followed 1,500 year older Egyptian theoretical arithmetic
tradition. Of course, many have disagreed by proposing that Greeks
'invented' the first western theoretical arithmetic.

Today, to avoid the Greek debate, due to the lack of Greek texts, the
Babylonian algorithmic metaphor is often used alongside the "Dedekind
Cut" to define our modern theoretical base 10 decimal arithmetic.

However, beneath the 'arrow of time', the circle, and other theoretical
arithmetic proposals, lie four simple truths. Mathematicians at no time
invented the four arithmetic operations. Only applications of the four
arithmetic operations have been discussed by Dedekind, the Chinese,
Greeks, Egyptians, Babylonians and others.

Best Regards,

Milo Gardner

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