Re: Computability

On Wed, 9 Jan 2008 02:29:19 -0800 (PST), The Dougster 22044
<DGoncz@xxxxxxxxxxxx> wrote:

Well, visions of global one-ness aside, maybe I should just rewrite
the proposition this way:

A x,y,z,k in Z,
(x,y) = (y,z) = (x,z) = 1 ==>
!E k | A (a,b,c) in S={ (x,y,z),(x,z,y), ... (z,y,x) )
o(a * i(b,c), c) = k

On the other hand, maybe nobody here cares.

Maybe nobody fully understands your notation.

Suggestion -- unless you are deliberately trying to reduce the pool of
potential responders, you should not use obscure abbreviations, even
if that means it takes you a little longer to write the post. Your
goal should be clarity. Thus, not too compact, not too wordy -- try to
find a natural balance.

I'll offer a constructive critique of your style ...

In your first line,

"A x,y,z"

means what?

Presumable "A" denotes "for all"?

Then why not say "For all x,y,z"?

A few extra characters is not too wordy.

Most math books don't use the upside down A for statements. Why not?
To avoid notational weirdness, that's why. Have empathy for your
readers. Of course, for books on logic, model theory, set theory and
related subjects, the quantifier symbols are an essential part of the
underlying language, so that's a different story.

But in any case, no math book that I'm aware of uses the ordinary
alphabetic symbol "A" to denote "for all".

So I would write your first line as:

"For all x,y,z,k in Z"

The symbol "Z" for the integers is fine.

Same objection with regard to

"!E k"

Presumably you mean "there exists a unique k".

Once again, I would use the words. After all, it's a one time thing.
It would be different if the same phrase "there exists a unique" was
being used again and again -- that would seem to justify an
abbreviation.

Since you are one writer, writing for multiple readers, you should
make it easy for them, not for yourself.

Your last line

"o(a * i(b,c), c) = k"

is gibberish to me.

I would guess "o" denotes "order of", but order of what, and with
respect to what?

I have no idea what the 3 arguments to "o" represent.

I have no clue what i(b,c) means.

All in all, an obscure post.

Why should I bother struggling to decipher it when it appears you have
made no effort to reach anyone except those who already know what you
are talking about.

A few simple numerical examples might have made up for the coded
wording. Your original post suggests that you have such examples. Why
did you not bother to share them? Remember -- one writer, multiple
readers. A little extra effort on your part (one person) benefits all
the readers (many people). Empathize with the many, and be generous
with your explanatory efforts (within reason).

Ok, that's my critique.

Perhaps it will help you improve your writing style.

quasi
.

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