Re: Does the Calculus rest on Euclid?

In article <f8ydndgFObkD5hPZnZ2dnUVZ_rWdnZ2d@xxxxxxxxxxxxx>,
Hatto von Aquitanien <abbot@xxxxxxxxxxxxxx> wrote:

Virgil wrote:

In article <76ednSWq78NhjBPZnZ2dnUVZ_tOdnZ2d@xxxxxxxxxxxxx>,
Hatto von Aquitanien <abbot@xxxxxxxxxxxxxx> wrote:

Mike Kelly wrote:

Carefully reviewing to check for contradictions, eh? Why did nobody
ever think to try doing that before? I suppose they didn't have your
intuition to guide them.


"It is not the purpose of this work to cover the "firm rock" upon which
the house of analysis is founded with a fake wooden structure of
formalism - a structure that can fool the reader and, ultimately, the
author into
believing that it is the true foundation. Rather I shall show that this
house is to a large degree build on sand" - Hermann Weyl

A good deal of concrete has been intermixed with that sand since Weyl's
time. That was over 50 years ago.

I note that Dededkind and Cauchy, whose names were invoked in this
discussion, preceded Weyl.

Weyl died in 1955. Presumably the work cited above was published before
that so that there has been over half a century of progress since.

Or does Hatto believe that nothing has been done at all in the last half
century?


It is also possible that the problem I perceive
has been dealt with by introducing an assumption (axiom) with which I would
agree. But that seems unlikely since to me, proving the continuity of real
numbers is like proving the existence of the Universe.

Depends on what one means by continuity.

WE have no idea what YOU mean by it.
.