Re: Dedekind Cuts, Fundamental Sequences: why?

Glen Wheeler a écrit :
"Hatto von Aquitanien" <abbot@xxxxxxxxxxxxxx> wrote in message news:FqWdncA-GfEgP_HbnZ2dnUVZ_g-dnZ2d@xxxxxxxxxxxxxxxx
Booting is shortened from "bootstrapping" which is a euphemism meaning to
lift oneself by one's own bootstraps. A similar situation arrises when we
get the latest source code for gcc (the gnu compiler collection). In order
to get a compiler from the source code we have to compile the compiler.
The only way to compile the compiler is with a compiler. These are all
examples of a self-referential system. The ultimate example of the
self-referential problem in Russell's Paradox. I am quite confident that
such a self-reference is at the core of the difficulty in defining the real
numbers in terms of the rational numbers.


The only difficulty my friend is in your mind. There are many ways to define the reals that do not presuppose the existence of the reals. See for example (IIRC) Seaman's message and my reply for two consistent methods.

At this point in the thread, you are simply trolling.

Was it ever otherwise?


All of this is
covered (at least in Australia, I presume other countries are at least as good if not better) in a second year, compulsory analysis course.

.

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