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Topic: Non-Euclidean Arithmetic
Replies: 33   Last Post: Sep 21, 2012 2:48 PM

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 Paul A. Tanner III Posts: 5,920 Registered: 12/6/04
Re: Non-Euclidean Arithmetic
Posted: Sep 13, 2012 5:54 PM

On Thu, Sep 13, 2012 at 10:22 AM, Joe Niederberger
<niederberger@comcast.net> wrote:
> Paul Tanner III
>>The term can be used in more than one way. When I said "name" I meant, for sake of simplicity as I explicitly said, instead of saying (x,0) just say x.
>
> You don;t understand. There aren't enough name likes
> x, x, z, x', x'' etc. Those are countable -- leading to a terribly unfair game of musical chairs. The vast majority of reals are unnameable and undefinable, lost souls waiting for someone kindhearted to pity them.
>
> Your "process" is no process at all, it has 0% chance of being carried out in general. It has a big "gotcha!" that you blithely skip over ("A Miracle Happens Here!)
>
> Even phrases like "W.L.O.G." won't make this pig sing.
>
> For the countable set of numbers that are amenable to a process leading to an answer (find the product of two numbers,) you will find iteration or recursion absolutely necessary one way or another.
>
> In defense of similar triangles I will say I'm not against imaginary procedures that cannot really be carried out. They may even lead someone to carry out a simulacrum of the unreal procedure in the real world. The real world versions only work for a finite number of limited precision numbers though, and in the engraving of various scales (that word!) an iteration procedure was involved somewhere along the line.
>
>

"It's a process only if it's a computation" and "it exists only if
it's computable" exist only in a small mind.

Look them up and be educated:

http://en.wikipedia.org/wiki/Without_loss_of_generality

http://dictionary.reference.com/browse/process

A proof is a process, especially a constructive proof like the one I gave in

http://mathforum.org/kb/message.jspa?messageID=7889634

of how to construct the location of product ab on the real number line
from being given the locations of 1, a, and b on the real number line,
where a and b are arbitrary reals.