Re: JSH: Critique means slow, and thorough

Will Twentyman <wtwentyman@xxxxxxxxxxx> writes:

> jstevh@xxxxxxx wrote:
>> Again, for those who wonder what the latest discussion is about, if you
>> append 1/2 to the ring of integers, you get the reals--if you allow
>> infinite sums.
>>
>
> James, in this post you have claimed the following:
>
> 1) Z[1/2] is in the rationals.

He didn't claim that, did he?

> 2) Z[1/2] = reals
> 3) pi is not rational.
>
> The only conclusion that can be drawn is that pi is not a real number.
> Are you sure that's what you want to claim?

Here's my guess.

Z is a subset of Q.

Q contains 1/2.

Z[1/2] is a superset of Q.

Therefore, Z[1/2] is not the minimal ring containing 1/2 and a
superset of Z.

If you try to add 1/2 to Z, you automatically overshoot Q. Now, if
you *start* with Q and "add" 1/2 to Q, probably you stay with Q. So
the process of adjoining elements to rings is non-monotonic (and a
touch unpredictable).

Anyway, that's my guess.

--
Jesse F. Hughes
"Wiles made somewhere around half a million dollars U.S. that I heard
about, and I know he didn't take major endorsements."
--JSH on the rewards of proving Fermat's last theorem.
.

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