Re: JSH: Critique means slow, and thorough



jstevh@xxxxxxx wrote: 
W. Dale Hall wrote:

jstevh@xxxxxxx wrote:

William Hughes wrote:


jst...@xxxxxxx wrote:


Adjoining such an element gives you the field of reals.

Now this issue has come up before, where I've noted that even 

doing

something as simple as adjoining 1/2 to the ring of integers will 

give


you reals. 

Have you noticed that the field of rational numbers contains Z[1/2]?



Yup.  And I've previously posted on the subject.


Why haven't you been railing about the "flaw" in the rational 

numbers?

Pi is rational!



No, pi is not rational.

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.
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?
--
Will Twentyman
email: wtwentyman at copper dot net
.

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