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Topic: Analytic vs. Synthetic Geometry
Replies: 7   Last Post: Sep 5, 2013 10:55 PM

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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: Analytic vs. Synthetic Geometry
Posted: Sep 5, 2013 10:03 AM
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Lite Beta wrote:

> Also, R^n is the Cartesian product. So isn't it by default that the n numbers in R^n are cartesian coordinates?

It seems to me that "R^n" is ambiguous, it might be nothing more than
this set: {(x_1,...,x_n): x_i real, 1 <= i <= n}. Or it might be that
set with structure on it. In the latter case, there are various
possible structures: additive group, vector space, metric space,...

Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies

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