Re: Does the Calculus rest on Euclid?

Hatto von Aquitanien wrote:

If a real number is a "set of rationals", and there is only one real number
designated by the concept indicated by the phrase "a real number", then, in
the case of pi either the set called pi is identical to the object called
pi, or we are avoiding (or more correctly, evading) the original topic.

It doesn't make sense to talk about what the object called pi "is".
Numbers don't exist in the same sense as the pen sitting on my desk.
Certain properties characterize pi, and especially its properties as a
member of the set of all real numbers. In different models of the real
numbers, pi might be a set of rational numbers, an equivalence class of
sequences of rational numbers, or even a point on a line. Whether or
not these objects are "identical" is irrelevant. The point is that all
these models behave equivalently in the ways that are significant for
real numbers. What color is pi? It doesn't matter.

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