Re: JSH: Short explanation, why error is so big

On 9 Dec 2006 11:10:55 -0800, jstevh@xxxxxxx wrote:

jankrihau@xxxxxxxxxxx wrote:
jstevh@xxxxxxx wrote:
Well, mathematicians over a hundred years ago when algebraic integers
were discovered, thought that what was true with algebraic integers was
true in general, so to them 7 is NOT a factor of a_2(x), and somehow
the 7 is getting split up, and they built mathematical ideas they
thought were proofs on the flawed belief.

Please provide a reference for this claim: "what is true with algebraic
integers is true in general".

---
J K Haugland
http://home.no.net/zamunda

Ok, maybe I'm wrong. I've been told this by posters on math
newsgroups,

No, you have not been told this.

so let's check.

For the sake of argument, consider the result that whether or not an
algebraic integer has some number as a factor in the ring of algebraic
integers means nothing important mathematically.

Ok, let's assume that. Note that this assumption cannot possibly have
any effect whatever on the truth or falsity of any mathematical
result, because whether or not something is "important" is not a
mathematical question.

Just like it doesn't matter that 2 is not a factor of 6 with evens
because we know it is a factor of 6 as 6 = 2*3.

Just like this statement. Here are two true facts:

(i) 2 is not a factor of 6 in the ring of even integers

(ii) 2 is a factor of 6 in the ring of integers.

Fine. But the statement "(i) doesn't matter because of (ii)"
has no mathematical content whatever.

So let's say that now,
for the sake of argument, it is clear that the ring of algebraic
integers and results in that ring don't matter.

Would that impact any arguments accepted as proofs in the mathematical
field?

No, it can't possibly have any such impact, because it's not
a mathematical statement.

James Harris


************************

David C. Ullrich
.

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