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On 29 Sep 2006 19:11:48 -0700, jstevh@xxxxxxx wrote:
>Some recent threads simply explaining yet another way to see the
>coverage problem of the ring of algebraic integers have floundered on
>the issue of convergence and what it means with rings like the ring of
>algebraic integers, where I introduce the concept of an exclusionary
>ring.
>
>The concepts are simple, luckily, as I can mostly use something basic:
>[explanation of the utterly non-shocling fact that an infinite
>series of algenraic integers can have sum not equal to an algebraic
>integer snipped]
>
>If any of you actually know mathematics versus being people who can
>repeat what you're told as if that's all that matters, then you can
>explain the status quo view.
The "status quo view", more commonly known as the facts of the matter,
is that there's simply no problem with this. Yes, you can have an
infinite series where all the terms are algebraic integers and
the series converges to something other than an algebraic integer.
This is incredibly well-known. And it's simply not a problem,
unless for some reason you've decided that that's not the way
things should be. If so that's _your_ problem.
>You can explain the mainstream beliefs of the mathematical community in
>this area without relying on insults, without simply claiming that I'm
>wrong, and without doing anything other than objectively replying.
Assuming one reads what you wrote generously, the mathematical
facts you've stated are not wrong. What's wrong is the idea that
this is some sort of problem. And what's _really_ wrong is the
idea that you've discovered something that the mathematicians
have not noticed, or noticed but tried to cover up, or
whatever the heck your point is.
See, to demonstrate that your point somehow contradicts standard
mathematics you need to find someone somewhere claiming that
things are _not_ as you say. Go ahead - find a statement somewhere
in the literature that states that if an infinite series converges
and the terms are all algebraic integers then the sum must
be an algebraic integer.
>I know that can't be done, so I say that upfront to remind readers that
>a lot of people around the world are fighting the truth
Very brave of you to say we're fighting the truth. Now what
are you going to do with all these replies that say instead
"yes, that's correct - so what?"
>with my
>research to preserve their delusion of expertise, which is all about a
>lot of people getting some mathematics wrong.
>
>
>James Harris
************************
David C. Ullrich
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