odd v. uneven

[occam]

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.

[Peter Moylan]

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

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

[occam]

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>

[Kerr-Mudd, John]

On Sun, 4 Dec 2022 16:01:23 +0100
occam <oc...@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.

[Bertel Lund Hansen]

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

[Athel Cornish-Bowden]

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.

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

[Bertel Lund Hansen]

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

[Richard Heathfield]

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

[Athel Cornish-Bowden]

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.

[bruce bowser]

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

[Bebercito]

Isn't it also divisible by 1 or 3?

>
> --
> Bertel

[Richard Heathfield]

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

[Bertel Lund Hansen]

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

[Bertel Lund Hansen]

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

[Paul Wolff]

On Sun, 4 Dec 2022, at 11:58:03, occam posted:

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

[Quinn C]

* Bebercito:

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

[Jerry Friedman]

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

[Peter Moylan]

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.

[Bebercito]

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

[Peter Moylan]

6 is also divisible by 3. How odd!

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

[occam]

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

[occam]

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.

[Richard Heathfield]

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.

[Hibou]

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?

[Richard Heathfield]

The proof is simple enough:

Horses have an even number of legs.

A horse has forelegs, and also two hind legs.

Fore plus two hind is six, thus a horse has six legs, which is a
very odd number of legs for a horse to have.

But the number must also be even.

No finite number is both even and odd.

Therefore, a horse has an infinite number of legs

[bert]

But that is the whole point, and the whole basis of Ramanujan's insight:
the mutual dependence between expressing a number as the sum of
two cubes and expressing it as a product of primes of the form 6n+1.

[Kerr-Mudd, John]

I meant to write 'twice as interesting' (map {0,i} to {0,2i} (probably
wrong notation, BYKWIM, I hope))

> in Peter's conjecture does not exist.
>
> [*] I like that a lot, a lot

If in doubt ask a lotl.

[Peter Moylan]

The version I know goes on at greater length.

LEMMA: All horses are the same colour.

PROOF: By induction. Suppose that we have proved that any set of N
horses has the same colour. (The case N=1 is trivial.) Now consider a
set of N+1 horses. Remove one of them. The remainder have the same
colour, by the inductive argument. Now put that one back, and remove a
different one. Again, the remaining N horses have the same colour.
Therefore, this set of N+1 horses has the same colour.

THEOREM: All horses have an infinite number of legs.

PROOF 1: As outlined above by Richard.

PROOF 2: In case you find Proof 1 unconvincing, here is another approach
to the same result.

Suppose that somewhere there is a poor crippled horse with only a finite
number of legs. That would be a horse of a different colour, and that's
impossible by the Lemma.

[Richard Heathfield]

* applause *

[occam]

...followed by a di-lemma. What colour horse should I bet on at the next
Grand National?

[lar3ryca]

I wandered lonely as a clod.
Just picking up old rags and bottles.
As onward on my way I plod,
I saw a host of axolotls.

--
Yeah, Windows is great... I used it to download Linux.

[Tak To]

On 12/4/2022 12:47 PM, Bertel Lund Hansen wrote:
> 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".

Classical Chinese has 奇 <ji1> "strange, unusual" and 偶 <ou3>
"spouse".

Middle to Modern Chinese has 單 <dan1> "single" and 雙 <shuang2>
"double".

--
Tak
----------------------------------------------------------------+-----
Tak To ta...@alum.mit.eduxx
--------------------------------------------------------------------^^
[taode takto ~{LU5B~}] NB: trim the xx to get my real email addr

[Peter Moylan]

On 06/12/22 06:45, lar3ryca wrote:

> I wandered lonely as a clod.
> Just picking up old rags and bottles.
> As onward on my way I plod,
> I saw a host of axolotls.

Beside the lake, beneath the trees
Enough to make a man's blood freeze.

[lar3ryca]

On 2022-12-05 19:10, Peter Moylan wrote:
> On 06/12/22 06:45, lar3ryca wrote:
>
>> I wandered lonely as a clod.
>> Just picking up old rags and bottles.
>> As onward on my way I plod,
>> I saw a host of axolotls.
>
> Beside the lake, beneath the trees
> Enough to make a man's blood freeze.

Some had handles, some were plain;
They came in blue, red pink, and green.

--
I'd give my right arm to be ambidextrous.

[Jerry Friedman]

On Monday, December 5, 2022 at 2:30:25 AM UTC-7, bert wrote:
> On Sunday, 4 December 2022 at 21:11:15 UTC, 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.

> But that is the whole point, and the whole basis of Ramanujan's insight:
> the mutual dependence between expressing a number as the sum of
> two cubes and expressing it as a product of primes of the form 6n+1.

More number theory I don't understand. But I take it you're talking
about odd "taxicab numbers", since for even numbers, 2 (obviously) and 3
can be prime factors as well.

http://oeis.org/A001235

--
Jerry Friedman

[Snidely]

Sunday, Bebercito observed:

It has an infinite number of prime factors.

/dps

--
Ieri, oggi, domani