An odd number is the same as an uneven number
yet,
an uneven surface is not an odd surface
furthermore,
an odd score is not the same thing an uneven score
yet,
an uneven playing field is not at all an odd thing

I find that odd, even if I say so myself.

On 04/12/22 21:58, occam wrote:
> An odd number is the same as an uneven number
> yet,
> an uneven surface is not an odd surface
> furthermore,
> an odd score is not the same thing an uneven score
> yet,
> an uneven playing field is not at all an odd thing
>
> I find that odd, even if I say so myself.

Let N be the first natural number that is not interesting ...

--
Peter Moylan Newcastle, NSW http://www.pmoylan.org

On 04/12/2022 12:09, Peter Moylan wrote:
> On 04/12/22 21:58, occam wrote:
>> An odd number is the same as an uneven number
>> yet,
>> an uneven surface is not an odd surface
>> furthermore,
>> an odd score is not the same thing an uneven score
>> yet,
>> an uneven playing field is not at all an odd thing
>>
>> I find that odd, even if I say so myself.
>
> Let N be the first natural number that is not interesting ...
>

Can we agree that all uneven numbers are interesting on the grounds that
they are odd, and all even numbers are quite interesting even if not as
odd as uneven numbers?

P.S.

<https://books.google.com/ngrams/graph?content=odd+number%2Cuneven+number&year_start=1800&year_end=2019&corpus=26&smoothing=3>

On Sun, 4 Dec 2022 16:01:23 +0100
occam <occam@nowhere.nix> wrote:

> On 04/12/2022 12:09, Peter Moylan wrote:
> > On 04/12/22 21:58, occam wrote:
> >> An odd number is the same as an uneven number
> >> yet,
> >> an uneven surface is not an odd surface
> >> furthermore,
> >> an odd score is not the same thing an uneven score
> >> yet,
> >> an uneven playing field is not at all an odd thing
> >>
> >> I find that odd, even if I say so myself.
> >
> > Let N be the first natural number that is not interesting ...
> >
>
> Can we agree that all uneven numbers are interesting on the grounds that
> they are odd, and all even numbers are quite interesting even if not as
> odd as uneven numbers?

What nonsense! Even numbers are /twice/ as odd as odd numbers!
>
> P.S.
>
> <https://books.google.com/ngrams/graph?content=odd+number%2Cuneven+number&year_start=1800&year_end=2019&corpus=26&smoothing=3>

--
Bah, and indeed Humbug.

Den 04.12.2022 kl. 16.54 skrev Kerr-Mudd, John:

>>>> An odd number is the same as an uneven number
>>>> yet,
>>>> an uneven surface is not an odd surface
>>>> furthermore,
>>>> an odd score is not the same thing an uneven score
>>>> yet,
>>>> an uneven playing field is not at all an odd thing
>>>>
>>>> I find that odd, even if I say so myself.
>>>
>>> Let N be the first natural number that is not interesting ...
>>>
>>
>> Can we agree that all uneven numbers are interesting on the grounds that
>> they are odd, and all even numbers are quite interesting even if not as
>> odd as uneven numbers?
>
> What nonsense! Even numbers are /twice/ as odd as odd numbers!

It takes a nerd to even think of with such an odd idea.

--
Bertel

On 2022-12-04 17:17:49 +0000, Bertel Lund Hansen said:

> Den 04.12.2022 kl. 16.54 skrev Kerr-Mudd, John:
>
>>>>> An odd number is the same as an uneven number
>>>>> yet,
>>>>> an uneven surface is not an odd surface
>>>>> furthermore,
>>>>> an odd score is not the same thing an uneven score
>>>>> yet,
>>>>> an uneven playing field is not at all an odd thing
>>>>>
>>>>> I find that odd, even if I say so myself.
>>>>
>>>> Let N be the first natural number that is not interesting ...
>>>>
>>>
>>> Can we agree that all uneven numbers are interesting on the grounds that
>>> they are odd, and all even numbers are quite interesting even if not as
>>> odd as uneven numbers?
>>
>> What nonsense! Even numbers are /twice/ as odd as odd numbers!
>
> It takes a nerd to even think of with such an odd idea.

We'll get even with you one of these days?

--
Athel -- French and British, living in Marseilles for 36+ years; mainly
in England until 1987.

Le dimanche 4 décembre 2022 à 11:58:08 UTC+1, occam a écrit :
> An odd number is the same as an uneven number
> yet,
> an uneven surface is not an odd surface
> furthermore,
> an odd score is not the same thing an uneven score
> yet,
> an uneven playing field is not at all an odd thing
>
> I find that odd, even if I say so myself.

What I find odd is that in many languages, numbers 1, 3, 5... are defined as the
negative of 2, 4, 6..., i.e. "un" + "even", "im" + "pair" (French), "gerade" + "un" + "gerade"
(German), etc. whereas 1 comes before 2 - so that the opposite would seem more
logical (assuming 0 is neither odd or even).

Den 04.12.2022 kl. 18.33 skrev Bebercito:

> What I find odd is that in many languages, numbers 1, 3, 5... are defined as the
> negative of 2, 4, 6..., i.e. "un" + "even", "im" + "pair" (French), "gerade" + "un" + "gerade"
> (German),

In Denmark "straight" and "unstraight".

> etc. whereas 1 comes before 2 - so that the opposite would seem more
> logical (assuming 0 is neither odd or even).

0 is even = divisible by 2

--
Bertel

On 04/12/2022 3:01 pm, occam wrote:
> On 04/12/2022 12:09, Peter Moylan wrote:
>> On 04/12/22 21:58, occam wrote:
>>> An odd number is the same as an uneven number
>>> yet,
>>> an uneven surface is not an odd surface
>>> furthermore,
>>> an odd score is not the same thing an uneven score
>>> yet,
>>> an uneven playing field is not at all an odd thing
>>>
>>> I find that odd, even if I say so myself.
>>
>> Let N be the first natural number that is not interesting ...
>>
>
> Can we agree that all uneven numbers are interesting on the grounds that

Peter's joke is that mathematicians would be extremely interested
by the first natural number that is not interesting (and thus we
have a contradiction).

--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

On 2022-12-04 17:55:02 +0000, Richard Heathfield said:

> On 04/12/2022 3:01 pm, occam wrote:
>> On 04/12/2022 12:09, Peter Moylan wrote:
>>> On 04/12/22 21:58, occam wrote:
>>>> An odd number is the same as an uneven number
>>>> yet,
>>>> an uneven surface is not an odd surface
>>>> furthermore,
>>>> an odd score is not the same thing an uneven score
>>>> yet,
>>>> an uneven playing field is not at all an odd thing
>>>>
>>>> I find that odd, even if I say so myself.
>>>
>>> Let N be the first natural number that is not interesting ...
>>>
>>
>> Can we agree that all uneven numbers are interesting on the grounds that
>
> Peter's joke is that mathematicians would be extremely interested by
> the first natural number that is not interesting (and thus we have a
> contradiction).

When Hardy visited Ramanujan in hospital he commented that the number
of his taxi, 1729, was rather an ordinary number. Ramanujan pointd out
that it is the smallest integer that can be expressed as the sum of two
cubes in two different ways. No matter how you define "ordinary" there
will always be some criterion by which it is interesting.

--
Athel -- French and British, living in Marseilles for 36+ years; mainly
in England until 1987.

On Sunday, December 4, 2022 at 12:17:53 PM UTC-5, Bertel Lund Hansen wrote:
> Den 04.12.2022 kl. 16.54 skrev Kerr-Mudd, John:
>
> >>>> An odd number is the same as an uneven number
> >>>> yet,
> >>>> an uneven surface is not an odd surface
> >>>> furthermore,
> >>>> an odd score is not the same thing an uneven score
> >>>> yet,
> >>>> an uneven playing field is not at all an odd thing
> >>>>
> >>>> I find that odd, even if I say so myself.
> >>>
> >>> Let N be the first natural number that is not interesting ...
> >>>
> >>
> >> Can we agree that all uneven numbers are interesting on the grounds that
> >> they are odd, and all even numbers are quite interesting even if not as
> >> odd as uneven numbers?
> >
> > What nonsense! Even numbers are /twice/ as odd as odd numbers!
>
> It takes a nerd to even think of with such an odd idea.

(forbedring)
It takes a nerd to even think of such an odd idea.
(no with)

Le dimanche 4 décembre 2022 à 18:47:32 UTC+1, Bertel Lund Hansen a écrit :
> Den 04.12.2022 kl. 18.33 skrev Bebercito:
>
> > What I find odd is that in many languages, numbers 1, 3, 5... are defined as the
> > negative of 2, 4, 6..., i.e. "un" + "even", "im" + "pair" (French), "gerade" + "un" + "gerade"
> > (German),
> In Denmark "straight" and "unstraight".
> > etc. whereas 1 comes before 2 - so that the opposite would seem more
> > logical (assuming 0 is neither odd or even).
> 0 is even = divisible by 2

Isn't it also divisible by 1 or 3?
>
> --
> Bertel

On 04/12/2022 6:03 pm, Athel Cornish-Bowden wrote:
> On 2022-12-04 17:55:02 +0000, Richard Heathfield said:
>
>> On 04/12/2022 3:01 pm, occam wrote:
>>> On 04/12/2022 12:09, Peter Moylan wrote:
>>>> On 04/12/22 21:58, occam wrote:
>>>>> An odd number is the same as an uneven number
>>>>> yet,
>>>>> an uneven surface is not an odd surface
>>>>> furthermore,
>>>>> an odd score is not the same thing an uneven score
>>>>> yet,
>>>>> an uneven playing field is not at all an odd thing
>>>>>
>>>>> I find that odd, even if I say so myself.
>>>>
>>>> Let N be the first natural number that is not interesting ...
>>>>
>>>
>>> Can we agree that all uneven numbers are interesting on the
>>> grounds that
>>
>> Peter's joke is that mathematicians would be extremely
>> interested by the first natural number that is not interesting
>> (and thus we have a contradiction).
>
> When Hardy visited Ramanujan in hospital he commented that the
> number of his taxi, 1729, was rather an ordinary number.
> Ramanujan pointd out that it is the smallest integer that can be
> expressed as the sum of two cubes in two different ways. No
> matter how you define "ordinary" there will always be some
> criterion by which it is interesting.

....although it may not seem so at first. Sometimes it takes a
Ramanujan to draw back the veil.

--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

Den 04.12.2022 kl. 19.03 skrev Athel Cornish-Bowden:

> When Hardy visited Ramanujan in hospital he commented that the number of
> his taxi, 1729, was rather an ordinary number. Ramanujan pointd out that
> it is the smallest integer that can be expressed as the sum of two cubes
> in two different ways.

Its primefactors are also interesting: 1729 = 7*13*19

The difference between them is 6.

--
Bertel

Den 04.12.2022 kl. 19.39 skrev Bebercito:

>> 0 is even = divisible by 2
>
> Isn't it also divisible by 1 or 3?

Of course. How is your definition of even numbers?

--
Bertel

On Sun, 4 Dec 2022, at 11:58:03, occam posted:
>An odd number is the same as an uneven number
>yet,
>an uneven surface is not an odd surface
>furthermore,
>an odd score is not the same thing an uneven score
>yet,
>an uneven playing field is not at all an odd thing
>
>I find that odd, even if I say so myself.

So do I, but there's a simple explanation. It is that you put your
commas on the wrong side of 'yet'.
--
Paul W

* Bebercito:

> Le dimanche 4 décembre 2022 à 11:58:08 UTC+1, occam a écrit :
>> An odd number is the same as an uneven number
>> yet,
>> an uneven surface is not an odd surface
>> furthermore,
>> an odd score is not the same thing an uneven score
>> yet,
>> an uneven playing field is not at all an odd thing
>>
>> I find that odd, even if I say so myself.
>
> What I find odd is that in many languages, numbers 1, 3, 5... are defined as the
> negative of 2, 4, 6..., i.e. "un" + "even", "im" + "pair" (French), "gerade" + "un" + "gerade"
> (German), etc. whereas 1 comes before 2 - so that the opposite would seem more
> logical (assuming 0 is neither odd or even).

So what? 1 is an incomplete pair, it's unbalanced. At two, you reach the
first level of completeness.

How odd is it to you that 10 is the first "round" number?

--
The least questioned assumptions are often the most questionable
-- Paul Broca
.... who never questioned that men are more intelligent than women

On Sunday, December 4, 2022 at 2:11:15 PM UTC-7, Bertel Lund Hansen wrote:
> Den 04.12.2022 kl. 19.03 skrev Athel Cornish-Bowden:
>
> > When Hardy visited Ramanujan in hospital he commented that the number of
> > his taxi, 1729, was rather an ordinary number. Ramanujan pointd out that
> > it is the smallest integer that can be expressed as the sum of two cubes
> > in two different ways.

> Its primefactors are also interesting: 1729 = 7*13*19
>
> The difference between them is 6.

Wikipedia lists other interesting facts about it.

https://en.wikipedia.org/wiki/1729_(number)

I have just learned that a sphenic number is one that is the product of
exactly three distinct primes. Good to know.

--
Jerry Friedman

On 05/12/22 02:01, occam wrote:
> On 04/12/2022 12:09, Peter Moylan wrote:
>> On 04/12/22 21:58, occam wrote:

>>> An odd number is the same as an uneven number yet, an uneven
>>> surface is not an odd surface furthermore, an odd score is not
>>> the same thing an uneven score yet, an uneven playing field is
>>> not at all an odd thing
>>>
>>> I find that odd, even if I say so myself.
>>
>> Let N be the first natural number that is not interesting ...

I should have mentioned that this is part of a classic proof that
"Everything is interesting". A later part of the proof uses an
assumption that I find questionable: if every number in a convergent
sequence is interesting, then the limit must also be interesting.

> Can we agree that all uneven numbers are interesting on the grounds
> that they are odd, and all even numbers are quite interesting even if
> not as odd as uneven numbers?

That actually comes up in the proof of a quite different theorem: that
all horses have an infinite number of legs.

--
Peter Moylan Newcastle, NSW http://www.pmoylan.org

Le dimanche 4 décembre 2022 à 22:12:16 UTC+1, Bertel Lund Hansen a écrit :
> Den 04.12.2022 kl. 19.39 skrev Bebercito:
>
> >> 0 is even = divisible by 2
> >
> > Isn't it also divisible by 1 or 3?
> Of course. How is your definition of even numbers?

Numbers that are divisible by 2 is a commonly admitted definition, but if 0 is also
divisible by odd numbers not themselves divisible by 2, why should it be considered
more even than odd?

>
> --
> Bertel

On 05/12/22 17:02, Bebercito wrote:
> Le dimanche 4 décembre 2022 à 22:12:16 UTC+1, Bertel Lund Hansen a écrit :
>> Den 04.12.2022 kl. 19.39 skrev Bebercito:
>>
>>>> 0 is even = divisible by 2
>>>
>>> Isn't it also divisible by 1 or 3?
>> Of course. How is your definition of even numbers?
>
> Numbers that are divisible by 2 is a commonly admitted definition, but if 0 is also
> divisible by odd numbers not themselves divisible by 2, why should it be considered
> more even than odd?

6 is also divisible by 3. How odd!

How many different divisors do you have to consider for a definition of
evenness?

--
Peter Moylan Newcastle, NSW http://www.pmoylan.org

On 04/12/2022 18:55, Richard Heathfield wrote:
> On 04/12/2022 3:01 pm, occam wrote:
>> On 04/12/2022 12:09, Peter Moylan wrote:
>>> On 04/12/22 21:58, occam wrote:
>>>> An odd number is the same as an uneven number
>>>> yet,
>>>> an uneven surface is not an odd surface
>>>> furthermore,
>>>> an odd score is not the same thing an uneven score
>>>> yet,
>>>> an uneven playing field is not at all an odd thing
>>>>
>>>> I find that odd, even if I say so myself.
>>>
>>> Let N be the first natural number that is not interesting ...
>>>
>>
>> Can we agree that all uneven numbers are interesting on the grounds that
>
> Peter's joke is that mathematicians would be extremely interested by the
> first natural number that is not interesting (and thus we have a
> contradiction).
>

That remark was not lost on me. There are no such things l as
uninteresting natural numbers, at least to a mathematician. Hence my
reply (that all odd numbers are interesting) and J.K-M's corollary*
(that even numbers are twice as odd as uneven numbers) says that the 'N'
in Peter's conjecture does not exist.

[*] I like that a lot, a lot

On 05/12/2022 03:11, Peter Moylan wrote:
> On 05/12/22 02:01, occam wrote:
>> On 04/12/2022 12:09, Peter Moylan wrote:
>>> On 04/12/22 21:58, occam wrote:
>
>>>> An odd number is the same as an uneven number yet, an uneven
>>>> surface is not an odd surface furthermore, an odd score is not
>>>> the same thing an uneven score yet, an uneven playing field is
>>>> not at all an odd thing
>>>>
>>>> I find that odd, even if I say so myself.
>>>
>>> Let N be the first natural number that is not interesting ...
>
> I should have mentioned that this is part of a classic proof that
> "Everything is interesting". A later part of the proof uses an
> assumption that I find questionable: if every number in a convergent
> sequence is interesting, then the limit must also be interesting.
>
>> Can we agree that all uneven numbers are interesting on the grounds
>> that they are odd, and all even numbers are quite interesting even if
>> not as odd as uneven numbers?
>
> That actually comes up in the proof of a quite different theorem: that
> all horses have an infinite number of legs.
>

I am getting more and more concerned that my Engineering Mathematics
class at university had gaping holes in its coverage. I cannot remember,
ever, coming across that last theorem.

On 05/12/2022 8:45 am, occam wrote:
> On 04/12/2022 18:55, Richard Heathfield wrote:
>> On 04/12/2022 3:01 pm, occam wrote:
>>> On 04/12/2022 12:09, Peter Moylan wrote:
>>>> On 04/12/22 21:58, occam wrote:
>>>>> An odd number is the same as an uneven number
>>>>> yet,
>>>>> an uneven surface is not an odd surface
>>>>> furthermore,
>>>>> an odd score is not the same thing an uneven score
>>>>> yet,
>>>>> an uneven playing field is not at all an odd thing
>>>>>
>>>>> I find that odd, even if I say so myself.
>>>>
>>>> Let N be the first natural number that is not interesting ...
>>>>
>>>
>>> Can we agree that all uneven numbers are interesting on the grounds that
>>
>> Peter's joke is that mathematicians would be extremely interested by the
>> first natural number that is not interesting (and thus we have a
>> contradiction).
>>
>
> That remark was not lost on me.

Sorry about that. As I'm sure you appreciate, it's increasingly
difficult to tell.

--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

Le 04/12/2022 à 10:58, occam a écrit :
>
> An odd number is the same as an uneven number
> yet,
> an uneven surface is not an odd surface
> furthermore,
> an odd score is not the same thing an uneven score
> yet,
> an uneven playing field is not at all an odd thing
>
> I find that odd, even if I say so myself.

But then, betting odds can be evens.

Isn't this just an example of a word with more than one sense having a
suitable number of antonyms?