Flash Gordon <spam@flash-gordon.me.uk> wrote:

> Malcolm McLean wrote, On 05/11/07 00:10:
>
> > As long as you've got an input and and output statement,
>
> Which in C use pointers, so you can only use them by using pointers.
> After all, stdin, stdout and stderr are pointers and when you call a
> function you are using a pointer to a function.
>
> > you can in fact
> > implement any program without pointers.
>
> In ALL languages? Even one where the only way to do input or output
> involves using a pointer?
>
> > That's a fundamental theorem.
>
> It is easy to prove that it is incorrect for at least one language.

It's Malcolm's usual muddle. The fundamental theorem, which has not even
been proved (though there is a great deal of circumstantial evidence for
it, and none against) is that any _calculation_ can be done on a Turing
machine. To leap from any calculation to any program is a bit of a long
one, though. Generally, programs have more requirements than that they
perform a single calculation.

Richard

Richard Bos wrote, On 05/11/07 11:15:
> Flash Gordon <spam@flash-gordon.me.uk> wrote:
>
>> Malcolm McLean wrote, On 05/11/07 00:10:
>>
>>> As long as you've got an input and and output statement,
>> Which in C use pointers, so you can only use them by using pointers.
>> After all, stdin, stdout and stderr are pointers and when you call a
>> function you are using a pointer to a function.
>>
>>> you can in fact
>>> implement any program without pointers.
>> In ALL languages? Even one where the only way to do input or output
>> involves using a pointer?
>>
>>> That's a fundamental theorem.
>> It is easy to prove that it is incorrect for at least one language.
>
> It's Malcolm's usual muddle. The fundamental theorem, which has not even
> been proved (though there is a great deal of circumstantial evidence for
> it, and none against) is that any _calculation_ can be done on a Turing
> machine.

That theorem I know, I just did not make the connection from what
Malcolm said. However, has anyone proved that C without pointers is
Turing complete? If not, then that needs to be done before Malcolm can
use that theorem.

> To leap from any calculation to any program is a bit of a long
> one, though. Generally, programs have more requirements than that they
> perform a single calculation.

Indeed.
--
Flash Gordon

Richard Bos said:

<snip>

> The fundamental theorem, which has not even
> been proved (though there is a great deal of circumstantial evidence for
> it, and none against)

Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
aren't you? If it's a theorem, it *has* been proved. If it has not been
proved, it is not a theorem. (Fermat's Last Theorem was for centuries a
misnomer, because it hasn't been proved. Now it's a misnomer because the
proof was supplied by Wiles, not Fermat.)

> is that any _calculation_ can be done on a Turing
> machine.

Wrong again! It's that any computable problem can be computed on a Turing
machine. Some problems are not computable. For example, the Halting
Problem (which we might express as "write a program that calculates
whether an arbitrary program (supplied at runtime) will eventually halt")
cannot be computed.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

Richard Heathfield wrote:

> Richard Bos said:
>
> <snip>
>
>> The fundamental theorem, which has not even
>> been proved (though there is a great deal of circumstantial evidence for
>> it, and none against)
>
> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
> aren't you? If it's a theorem, it *has* been proved. If it has not been
> proved, it is not a theorem.

Richard is referring (if I am not mistaken) to the Church-Turing /thesis/.

So you're right: it's not a theorem. (Off-hand, I recall it as too informal
to realistically expect a /proof/ of it.)

I don't think your position that unproved statements cannot be theorems
is sound, however, even if one discounts the fact that names that look
like descriptions need not be accurate labels.

--
Chris "informality begets formality" Dollin

Hewlett-Packard Limited registered office: Cain Road, Bracknell,
registered no: 690597 England Berks RG12 1HN

Chris Dollin <chris.dollin@hp.com> writes:

> Richard Heathfield wrote:
>
>> Richard Bos said:
>>
>> <snip>
>>
>>> The fundamental theorem, which has not even
>>> been proved (though there is a great deal of circumstantial evidence for
>>> it, and none against)
>>
>> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
>> aren't you? If it's a theorem, it *has* been proved. If it has not been
>> proved, it is not a theorem.

What a load of rubbish.

Fermat's last theorem wasn't "proven" until 1994.

>
> Richard is referring (if I am not mistaken) to the Church-Turing /thesis/.
>
> So you're right: it's not a theorem. (Off-hand, I recall it as too informal
> to realistically expect a /proof/ of it.)
>
> I don't think your position that unproved statements cannot be theorems
> is sound, however, even if one discounts the fact that names that look
> like descriptions need not be accurate labels.

Chris Dollin said:

<snip>

> Richard is referring (if I am not mistaken) to the Church-Turing
> /thesis/.

Indeed.

> So you're right:

Natch. :-)

> it's not a theorem. (Off-hand, I recall it as too
> informal to realistically expect a /proof/ of it.)
>
> I don't think your position that unproved statements cannot be theorems
> is sound, however, even if one discounts the fact that names that look
> like descriptions need not be accurate labels.

This, however, is interesting. If I'm wrong, two useful things happen:

1) I get egg all over my face for incorrectly tweaking RB's nose;
2) I learn something.

Nevertheless, alas, I am not yet convinced that I am wrong. Not being a
mathematician, I have little recourse but to look at the mathematical
equivalent of Wikipedia and hope that it's a bit more accurate. Here is
what it has to say about theorems:

"A theorem is a statement that can be demonstrated to be true by accepted
mathematical operations and arguments. In general, a theorem is an
embodiment of some general principle that makes it part of a larger
theory. The process of showing a theorem to be correct is called a proof."

The case for the defence rests, m'lud.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

[citation needed!]

Richard Heathfield said:

> Nevertheless, alas, I am not yet convinced that I am wrong. Not being a
> mathematician, I have little recourse but to look at the mathematical
> equivalent of Wikipedia

....by which I was intending to refer to "mathworld.wolfram.com" - apologies
for the omission.

> and hope that it's a bit more accurate

(that is, more accurate than the Wikipedia equivalent of Wikipedia!)

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

Richard Heathfield wrote:

> Chris Dollin said:
>
> <snip>
>
>> Richard is referring (if I am not mistaken) to the Church-Turing
>> /thesis/.
>
> Indeed.
>
>> So you're right:
>
> Natch. :-)
>
>> it's not a theorem. (Off-hand, I recall it as too
>> informal to realistically expect a /proof/ of it.)
>>
>> I don't think your position that unproved statements cannot be theorems
>> is sound, however, even if one discounts the fact that names that look
>> like descriptions need not be accurate labels.
>
> This, however, is interesting. If I'm wrong, two useful things happen:
>
> 1) I get egg all over my face for incorrectly tweaking RB's nose;
> 2) I learn something.
>
> Nevertheless, alas, I am not yet convinced that I am wrong. Not being a
> mathematician, I have little recourse but to look at the mathematical
> equivalent of Wikipedia and hope that it's a bit more accurate. Here is
> what it has to say about theorems:
>
> "A theorem is a statement that can be demonstrated to be true by accepted
> mathematical operations and arguments. In general, a theorem is an
> embodiment of some general principle that makes it part of a larger
> theory. The process of showing a theorem to be correct is called a proof."

"Can be demonstrated [to be true]" is wishful thinking. "Has been demonstrated,
as best as we can tell" is nearer the mark. Which means there can be (and
have been) "theorems" that are unproven because their proofs turn out to
be buggy. Rather than theoremhood being instantaneously removed from the
statement, debugging happens. Hence my claim:

>> I don't think your position that unproved statements cannot be theorems
>> is sound

It's certainly /desirable/ that theorems have valid proofs; I'm not
saying there are /lots/ of unproven theorems around, or that it's
desirable that there be unproven theorems; I'm just saying that /insisting/
that some statement has, right now, a unholed proof, in order to be (called)
a theorem, is a tad on the strong side.

That's my assessment from the reading around maths that I've done. If there
are actual practicing mathematicians reading here who can offer current
practice, I'm willing to take over Richard H's egg.

--
Chris "preferably not ostrich" Dollin

Hewlett-Packard Limited registered office: Cain Road, Bracknell,
registered no: 690597 England Berks RG12 1HN

Chris Dollin wrote:
>
> Richard Heathfield wrote:

> > Oh my dear chap,
> > you're beginning to make a bit of a habit of being wrong,
> > aren't you? If it's a theorem, it *has* been proved.
> > If it has not been proved, it is not a theorem.
>
> Richard is referring (if I am not mistaken)
> to the Church-Turing /thesis/.

I don't know about that, but my entire tenth grade math education
consisted of memorizing a few axioms
and proofs of ten fundamental theorems,
which I then used to proove other theorems
and so on and so forth, for the rest of the year.

In physics the following year,
I learned of the hierarchy of observation, conjecture,
hypothesis, theory, and law;
in which "theories"
are not generally considered to have been prooven.

--
pete

On Nov 5, 9:26 am, Richard <rgr...@gmail.com> wrote:
> Chris Dollin <chris.dol...@hp.com> writes:
> > Richard Heathfield wrote:
>
> >> Richard Bos said:
>
> >> <snip>
>
> >>> The fundamental theorem, which has not even
> >>> been proved (though there is a great deal of circumstantial evidence for
> >>> it, and none against)
>
> >> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
> >> aren't you? If it's a theorem, it *has* been proved. If it has not been
> >> proved, it is not a theorem.
>
> What a load of rubbish.
>
> Fermat's last theorem wasn't "proven" until 1994.

And as eveyone an his dog is fond of pointing out
"Fermat's last theorem" was not actually a theorem until
after Wiles' proof.

How many legs does a horse have if you call a tail
a leg? Four, calling a tail a leg does not make a tail
a leg.

- William Hughes

Richard wrote:
> Chris Dollin <chris.dollin@hp.com> writes:
>
>> Richard Heathfield wrote:
>>
>>> Richard Bos said:
>>>
>>> <snip>
>>>
>>>> The fundamental theorem, which has not even
>>>> been proved (though there is a great deal of circumstantial evidence for
>>>> it, and none against)
>>> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
>>> aren't you? If it's a theorem, it *has* been proved. If it has not been
>>> proved, it is not a theorem.

The rest of RH's snipped paragraph goes on to say:

] (Fermat's Last Theorem was for centuries a
] misnomer, because it hasn't been proved. Now it's a misnomer because
] the proof was supplied by Wiles, not Fermat.)

> What a load of rubbish.
>
> Fermat's last theorem wasn't "proven" until 1994.

You chose to comment on a snipped quotation rather the original message,
which distorts the discussion somewhat. There's certainly a sense in
which you're both wrong. Fermat proved his last theorem before he wrote
it down (or so he said) but the proof was never recorded or was lost.
Whether that's enough for it to be called a theorem in a technical
sense, I've no idea.

On Nov 5, 1:30 pm, "J. J. Farrell" <j...@bcs.org.uk> wrote:
> Richard wrote:
> > Chris Dollin <chris.dol...@hp.com> writes:
>
> >> Richard Heathfield wrote:
>
> >>> Richard Bos said:
>
> >>> <snip>
>
> >>>> The fundamental theorem, which has not even
> >>>> been proved (though there is a great deal of circumstantial evidence for
> >>>> it, and none against)
> >>> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
> >>> aren't you? If it's a theorem, it *has* been proved. If it has not been
> >>> proved, it is not a theorem.
>
> The rest of RH's snipped paragraph goes on to say:
>
> ] (Fermat's Last Theorem was for centuries a
> ] misnomer, because it hasn't been proved. Now it's a misnomer because
> ] the proof was supplied by Wiles, not Fermat.)
>
> > What a load of rubbish.
>
> > Fermat's last theorem wasn't "proven" until 1994.
>
> You chose to comment on a snipped quotation rather the original message,
> which distorts the discussion somewhat. There's certainly a sense in
> which you're both wrong. Fermat proved his last theorem before he wrote
> it down (or so he said) but the proof was never recorded or was lost.
> Whether that's enough for it to be called a theorem in a technical
> sense, I've no idea.

It's extremely doubtful that Fermat ever had created such a proof,
written down or not.
If he had such a proof, why did he labor so intensely in the future,
for proofs of simple, special cases?
He did offer a correct proof for N=4, but never (for instance) for 3
or 5.

William Hughes wrote:
> On Nov 5, 9:26 am, Richard <rgr...@gmail.com> wrote:
>> Chris Dollin <chris.dol...@hp.com> writes:
>>> Richard Heathfield wrote:
>>>> Richard Bos said:
>>>> <snip>
>>>>> The fundamental theorem, which has not even
>>>>> been proved (though there is a great deal of circumstantial evidence for
>>>>> it, and none against)
>>>> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
>>>> aren't you? If it's a theorem, it *has* been proved. If it has not been
>>>> proved, it is not a theorem.
>> What a load of rubbish.
>>
>> Fermat's last theorem wasn't "proven" until 1994.
>
> And as eveyone an his dog is fond of pointing out
> "Fermat's last theorem" was not actually a theorem until
> after Wiles' proof.
>
> How many legs does a horse have if you call a tail
> a leg? Four, calling a tail a leg does not make a tail
> a leg.
>
> - William Hughes
>
>

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

the·o·rem /ˈθiərəm, ˈθɪərəm/ Pronunciation Key - Show Spelled
Pronunciation[thee-er-uhm, theer-uhm] Pronunciation Key - Show IPA
Pronunciation
–noun
1. Mathematics. a theoretical proposition, statement, or formula
embodying something to be proved from other propositions or formulas.
2. a rule or law, esp. one expressed by an equation or formula.
3. Logic. a proposition that can be deduced from the premises or
assumptions of a system.
4. an idea, belief, method, or statement generally accepted as true or
worthwhile without proof.
[Origin: 1545–55; < LL the�réma < Gk theréma spectacle, hence, subject
for contemplation, thesis (to be proved), equiv. to the�ré-, var. s. of
the�re�n to view + -ma n. suffix]


Can you read?
"something to be proved from other propositions or formulas" (1)

Wikipedia says:
"... On the other hand, a deep theorem may be simply stated, but its
proof may involve surprising and subtle connections between disparate
areas of mathematics. Fermat's last theorem is a particularly well-known
example of such a theorem"

Of course Wikipedia is nothing... but the evil empire
says:
http://encarta.msn.com/encyclopedia_...7/Theorem.html
<quote>
Theorem, proposition or formula in mathematics or logic that is provable
from a set of postulates and basic assumptions
<end quote>

But OF COURSE in c.l.c the ONLY opinion that counts is the opinion
of Heathfield even if he says nonsense or make affirmations
without any proof like above.

There are MANY meanings to the word "theorem" and in many it
is something to be PROVED.

There is one interesting (proven) theorem: Goedel proved that there are
an infinite number of theorems that are neither true or false, i.e.
they can never be proved in a given system of axioms.

Then those theorems are... well "UNPROVEN" theorems. PERIOD.



--
jacob navia
jacob at jacob point remcomp point fr
logiciels/informatique
http://www.cs.virginia.edu/~lcc-win32

"Flash Gordon" <spam@flash-gordon.me.uk> wrote in message
> That theorem I know, I just did not make the connection from what Malcolm
> said. However, has anyone proved that C without pointers is Turing
> complete? If not, then that needs to be done before Malcolm can use that
> theorem.
>
You need IO. However we can easily write a Turing machine in C using an
array, an index, and a set of states.
We can then implement a C interpreter with our Turing machine, and so we can
run programs written with pointers.

--
Free games and programming goodies.
http://www.personal.leeds.ac.uk/~bgy1mm

jacob navia wrote:
> William Hughes wrote:
>> On Nov 5, 9:26 am, Richard <rgr...@gmail.com> wrote:
>>> Chris Dollin <chris.dol...@hp.com> writes:
>>>> Richard Heathfield wrote:
>>>>> Richard Bos said:
>>>>> <snip>
>>>>>> The fundamental theorem, which has not even
>>>>>> been proved (though there is a great deal of circumstantial
>>>>>> evidence for
>>>>>> it, and none against)
>>>>> Oh my dear chap, you're beginning to make a bit of a habit of being
>>>>> wrong,
>>>>> aren't you? If it's a theorem, it *has* been proved. If it has not
>>>>> been
>>>>> proved, it is not a theorem.
>>> What a load of rubbish.
>>>
>>> Fermat's last theorem wasn't "proven" until 1994.
>>
>> And as eveyone an his dog is fond of pointing out
>> "Fermat's last theorem" was not actually a theorem until
>> after Wiles' proof.
>>
>> How many legs does a horse have if you call a tail
>> a leg? Four, calling a tail a leg does not make a tail
>> a leg.
>> - William Hughes
>
> http://dictionary.reference.com/browse/theorem
>
> the·o·rem /ˈθiərəm, ˈθɪərəm/ Pronunciation Key - Show Spelled
> Pronunciation[thee-er-uhm, theer-uhm] Pronunciation Key - Show IPA
> Pronunciation
> –noun
> 1. Mathematics. a theoretical proposition, statement, or formula
> embodying something to be proved from other propositions or formulas.
> 2. a rule or law, esp. one expressed by an equation or formula.
> 3. Logic. a proposition that can be deduced from the premises or
> assumptions of a system.
> 4. an idea, belief, method, or statement generally accepted as true
> or worthwhile without proof.
> [Origin: 1545–55; < LL the�réma < Gk theréma spectacle, hence, subject
> for contemplation, thesis (to be proved), equiv. to the�ré-, var. s. of
> the�re�n to view + -ma n. suffix]
>
>
> Can you read?
> "something to be proved from other propositions or formulas" (1)
>
> Wikipedia says:
> "... On the other hand, a deep theorem may be simply stated, but its
> proof may involve surprising and subtle connections between disparate
> areas of mathematics. Fermat's last theorem is a particularly well-known
> example of such a theorem"
>
> Of course Wikipedia is nothing... but the evil empire
> says:
> http://encarta.msn.com/encyclopedia_...7/Theorem.html
> <quote>
> Theorem, proposition or formula in mathematics or logic that is provable
> from a set of postulates and basic assumptions
> <end quote>
>
> But OF COURSE in c.l.c the ONLY opinion that counts is the opinion
> of Heathfield even if he says nonsense or make affirmations
> without any proof like above.

Why do you insist on making a fool of yourself with silly sarcasm like
this? You've found evidence that Heathfield's statement was wrong, and
you've presented it. Why follow it with this ridiculous nonsense? Crow
about proving him wrong if you like, but parading this big chip on your
shoulder just makes you look daft.

> There are MANY meanings to the word "theorem" and in many it
> is something to be PROVED.
>
> ...

On Nov 5, 1:53 pm, jacob navia <ja...@nospam.com> wrote:
> William Hughes wrote:
> > On Nov 5, 9:26 am, Richard <rgr...@gmail.com> wrote:
> >> Chris Dollin <chris.dol...@hp.com> writes:
> >>> Richard Heathfield wrote:
> >>>> Richard Bos said:
> >>>> <snip>
> >>>>> The fundamental theorem, which has not even
> >>>>> been proved (though there is a great deal of circumstantial evidence for
> >>>>> it, and none against)
> >>>> Oh my dear chap, you're beginning to make a bit of a habit of being wrong,
> >>>> aren't you? If it's a theorem, it *has* been proved. If it has not been
> >>>> proved, it is not a theorem.
> >> What a load of rubbish.
>
> >> Fermat's last theorem wasn't "proven" until 1994.
>
> > And as eveyone an his dog is fond of pointing out
> > "Fermat's last theorem" was not actually a theorem until
> > after Wiles' proof.
>
> > How many legs does a horse have if you call a tail
> > a leg? Four, calling a tail a leg does not make a tail
> > a leg.
>
> > - William Hughes
>
> http://dictionary.reference.com/browse/theorem
>
> the·o·rem / i r m, r m/ Pronunciation Key - Show Spelled
> Pronunciation[thee-er-uhm, theer-uhm] Pronunciation Key - Show IPA
> Pronunciation
> -noun
> 1. Mathematics. a theoretical proposition, statement, or formula
> embodying something to be proved from other propositions or formulas.
> 2. a rule or law, esp. one expressed by an equation or formula.
> 3. Logic. a proposition that can be deduced from the premises or
> assumptions of a system.
> 4. an idea, belief, method, or statement generally accepted as true or
> worthwhile without proof.
> [Origin: 1545-55; < LL the réma < Gk theréma spectacle, hence, subject
> for contemplation, thesis (to be proved), equiv. to the ré-, var. s. of
> the re n to view + -ma n. suffix]
>
> Can you read?
> "something to be proved from other propositions or formulas" (1)
>
> Wikipedia says:
> "... On the other hand, a deep theorem may be simply stated, but its
> proof may involve surprising and subtle connections between disparate
> areas of mathematics. Fermat's last theorem is a particularly well-known
> example of such a theorem"
>
> Of course Wikipedia is nothing... but the evil empire
> says:http://encarta.msn.com/encyclopedia_...7/Theorem.html
> <quote>
> Theorem, proposition or formula in mathematics or logic that is provable
> from a set of postulates and basic assumptions
> <end quote>
>
> But OF COURSE in c.l.c the ONLY opinion that counts is the opinion
> of Heathfield even if he says nonsense or make affirmations
> without any proof like above.
>
> There are MANY meanings to the word "theorem" and in many it
> is something to be PROVED.
>
> There is one interesting (proven) theorem: Goedel proved that there are
> an infinite number of theorems that are neither true or false, i.e.
> they can never be proved in a given system of axioms.
>
> Then those theorems are... well "UNPROVEN" theorems. PERIOD.

Actually, I agree with Jacob here. Here is a mathematical definition
of theorem, and I think it agrees with the general sense:
http://mathworld.wolfram.com/Theorem.html

Malcolm McLean wrote, On 05/11/07 21:54:
>
> "Flash Gordon" <spam@flash-gordon.me.uk> wrote in message
>> That theorem I know, I just did not make the connection from what
>> Malcolm said. However, has anyone proved that C without pointers is
>> Turing complete? If not, then that needs to be done before Malcolm can
>> use that theorem.
>>
> You need IO. However we can easily write a Turing machine in C using an
> array, an index, and a set of states.

When you use the array name it decays to a pointer, so you are still
using pointers.

> We can then implement a C interpreter with our Turing machine, and so we
> can run programs written with pointers.

Apart from the fact you have just used a pointer according to the
definition of the C language, since array indexing is defined in terms
of pointer arithmetic.
--
Flash Gordon

J. J. Farrell wrote:
>
> Why do you insist on making a fool of yourself with silly sarcasm like
> this? You've found evidence that Heathfield's statement was wrong, and
> you've presented it. Why follow it with this ridiculous nonsense? Crow
> about proving him wrong if you like, but parading this big chip on your
> shoulder just makes you look daft.
>

Well... you have a bit of truth here. The problem is that
I have the last discussions in my mind, and I can't
abstract from them so easily.

Last time Mr Heathfield got carried away saying that strncmp
wasn't a string copy function... Incredible. When confronted
with evidence from the standard text, and from the semantics of
strncmp he argued that away. What surprised me was that nobody
(besides santosh) was ready to contradict him.

Now, this theorem stuff is much more milder (it could be
just a stupid remark somewhere) but again, only a few
people dare contradict Him (with guru uppercase).

Anyway, maybe just taking a bit of fresh air will do
a good thing to forget c.l.c and discuss normally.


--
jacob navia
jacob at jacob point remcomp point fr
logiciels/informatique
http://www.cs.virginia.edu/~lcc-win32

pete said:

> Chris Dollin wrote:
>>
>> Richard Heathfield wrote:
>
>> > Oh my dear chap,
>> > you're beginning to make a bit of a habit of being wrong,
>> > aren't you? If it's a theorem, it *has* been proved.
>> > If it has not been proved, it is not a theorem.
>>
>> Richard is referring (if I am not mistaken)
>> to the Church-Turing /thesis/.
>
> I don't know about that, but my entire tenth grade math education
> consisted of memorizing a few axioms
> and proofs of ten fundamental theorems,
> which I then used to proove other theorems
> and so on and so forth, for the rest of the year.
>
> In physics the following year,
> I learned of the hierarchy of observation, conjecture,
> hypothesis, theory, and law;
> in which "theories"
> are not generally considered to have been prooven.

Yes, but there is a difference between a "theory" (which is a science
concept) and a "theorem" (which is a formal systems concept).

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

J. J. Farrell said:

> jacob navia wrote:

<snip>

>>
>> Wikipedia says:
>> "... On the other hand, a deep theorem may be simply stated, but its
>> proof may involve surprising and subtle connections between disparate
>> areas of mathematics. Fermat's last theorem is a particularly well-known
>> example of such a theorem"
>>
>> Of course Wikipedia is nothing... but the evil empire
>> says:
>> http://encarta.msn.com/encyclopedia_...7/Theorem.html
>> <quote>
>> Theorem, proposition or formula in mathematics or logic that is provable
>> from a set of postulates and basic assumptions
>> <end quote>
>>
>> But OF COURSE in c.l.c the ONLY opinion that counts is the opinion
>> of Heathfield even if he says nonsense or make affirmations
>> without any proof like above.
>
> Why do you insist on making a fool of yourself with silly sarcasm like
> this? You've found evidence that Heathfield's statement was wrong,

....evidence, perhaps, but not proof. On the subject of mathematics, I'd
back Wolfram over Encarta or Wikipedia any day of the week. I'd also back
mathematicians such as Douglas Hofstadter over those sources. Here is his
definition of "theorem": "It means some statement in ordinary language
which has been proven to be true by a rigorous argument" - if Jacob Navia
wishes to argue with Hofstadter's and Wolfram's position on the matter,
that's up to him, but to claim that it is my *opinion* is simply wrong,
just as it would be wrong to say that it's my *opinion* that Dennis
Ritchie's middle initial is M.

Please also note that, whatever Mr Navia seems to think, I have never
claimed (unless, perhaps, in jest) that my opinion is normative in this
newsgroup.


--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

user923005 said:

<snip>

> Actually, I agree with Jacob here. Here is a mathematical definition
> of theorem, and I think it agrees with the general sense:
> http://mathworld.wolfram.com/Theorem.html

That is precisely the source that I quoted upthread. So you agree with me,
and you agree with Jacob. Therefore, Jacob agrees with me. QED.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

jacob navia <jacob@nospam.com> writes:
> J. J. Farrell wrote:
>> Why do you insist on making a fool of yourself with silly sarcasm
>> like this? You've found evidence that Heathfield's statement was
>> wrong, and you've presented it. Why follow it with this ridiculous
>> nonsense? Crow about proving him wrong if you like, but parading
>> this big chip on your shoulder just makes you look daft.
>
> Well... you have a bit of truth here. The problem is that
> I have the last discussions in my mind, and I can't
> abstract from them so easily.

Try harder.

> Last time Mr Heathfield got carried away saying that strncmp
> wasn't a string copy function... Incredible. When confronted
> with evidence from the standard text, and from the semantics of
> strncmp he argued that away. What surprised me was that nobody
> (besides santosh) was ready to contradict him.

Neither of the first two arguments to strncpy() needs to be a pointer
to a string. The fact that its name starts with "str", or that it's
in the "String handling" section of the standard, doesn't make it a
string function.

How exactly do you define the term "string function"?

> Now, this theorem stuff is much more milder (it could be
> just a stupid remark somewhere) but again, only a few
> people dare contradict Him (with guru uppercase).

Oh, good grief. There seem to be several different definitions of the
word "theorem". Richard's statement may or may not have been 100%
correct, but it was not unreasonable.

People tend not to agree with Richard Heathfield when he's right.

> Anyway, maybe just taking a bit of fresh air will do
> a good thing to forget c.l.c and discuss normally.

Good idea.

--
Keith Thompson (The_Other_Keith) kst-u@mib.org <http://www.ghoti.net/~kst>
Looking for software development work in the San Diego area.
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"

Keith Thompson said:

<snip>

> People tend not to agree with Richard Heathfield when he's right.

Yeah, I noticed that too.

Unfortunately, they don't agree with me when I'm wrong, either. If they
did, life would be so much simpler.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999