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Topic: Rudin and nonsense
Replies: 29   Last Post: May 3, 2012 9:46 PM

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 Paul A. Tanner III Posts: 5,920 Registered: 12/6/04
Re: Rudin and nonsense
Posted: May 3, 2012 2:48 AM

On Wed, May 2, 2012 at 7:10 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>This statement of yours "you could use the same technique to show any number of isomorphism collapsed into full equality" shows that you don't understand.
>
> Paul, I said "any number" NOT "every" or "all".
>
> Do you think the situation between R, C, isomorphisms, and rings are unique in regards to your argument? Publish that then, and solve even more millennium problems!
>
> But, forget that now, and please show how its possible in the very specific constructions I was alluding to, regarding C as made of "Kuratowski Pairs" of real numbers, that an element (set) could ever be equal to a "pair" in which it is also a member. That is, how is it possible under those conditions that EVER x = (x,0) for any x?
>
> Joe N

Since I have no idea what you think my "argument" is, I'll tell you what my "argument" is. Yet again: I accept as true Rudin's Theorem 1.29. Period. No more, no less. If you claim that I argue something else, then you are not telling the truth.

Rudin's Theorem 1.29 says that the equality (a,b) = a + bi is true for ALL real numbers a and b. That means for ALL substitution instances of a and b, including where we replace b with 0:

(a,0) = a + 0i = a + 0 = a.

To deny even just one substitution instance of Theorem 1.29 is to deny that the theorem is true, since the theorem is a claim that the equality in question is true for ALL substitution instances of the variables over the domain of the variables. That is: It is a contradiction to accept the truth of the equality in 1.29 ((a,b) = a + bi) for all real number values of b and then turn around and reject the truth of this equality where the value of b is real number 0. And so, if you deny the equality (a,b) = a + bi where the value of b is real number 0, then you deny Theorem 1.29, which again is the claim that this equality is true for ALL real number values of b.

The burden of proof is on you if you deny established, conventional, mathematics held to be true by professional mathematicians who specialize in analysis, like Theorem 1.29. I have no burden of proof, since my "argument" is simply to accept established, conventional mathematics held to be true by professional mathematicians who specialize in analysis, like Theorem 1.29.

The following link is relevant here:

http://en.wikipedia.org/wiki/Crank_(person)

Quote: ""Crank" is a pejorative term used for a person who unshakably holds a belief that most of his or her contemporaries consider to be false.[1] A crank belief is so wildly at variance with those commonly held as to be ludicrous to many. Cranks characteristically dismiss all evidence or arguments which contradict their own unconventional beliefs, making rational debate an often futile task; this is the essential defining characteristic of the crank: being impervious to facts, evidence, and rational inference."

Therefore your own statement "Publish that then, and solve even more millennium problems!" applies to you if you claim to have some great insight missed by the whole community of professional mathematicians who specialize in analysis with respect to Rudin's Theorem 1.29. That is, if you think that your Kuratowski stuff somehow shows that Rudin's Theorem 1.29 is false, then practice what you preach: "Publish that then, and solve even more millennium problems!"