See the following description here [1]:

```
In mathematics, a module is a generalization of the notion of vector space, wherein the field of scalars is replaced by a ring. The concept of module is also a generalization of the one of abelian group, since the abelian groups are exactly the modules over the ring of integers.
```
In the above narration, is the "a generalization of the one of abelian group" a good style?

[1] https://en.wikipedia.org/wiki/Module_(mathematics)

Regards,
HZ

On 5/7/2022 9:54 PM, hongy...@gmail.com wrote:
> See the following description here [1]:

> ``` In mathematics, a module is a generalization of the notion of
> vector space, wherein the field of scalars is replaced by a ring.
> The concept of module is also a generalization of the one of abelian
> group, since the abelian groups are exactly the modules over the
> ring of integers. ``` In the above narration, is the "a
> generalization of the one of abelian group" a good style?

> [1] https://en.wikipedia.org/wiki/Module_(mathematics)

No. It is also unclear, which is worse.

If the word "one" is intended to stand for "notion", the word
"notion" should be used there.

On 2022-05-08 01:54:00 +0000, hongy...@gmail.com said:

> See the following description here [1]:
>
> ```
> In mathematics, a module is a generalization of the notion of vector
> space, wherein the field of scalars is replaced by a ring. The concept
> of module is also a generalization of the one of abelian group, since
> the abelian groups are exactly the modules over the ring of integers.```
> In the above narration, is the "a generalization of the one of abelian
> group" a good style?

No. It's almost unintelligible.
>
> [1] https://en.wikipedia.org/wiki/Module_(mathematics)

I've changed "one" to "notion", as suggested by CDB.

--
Athel -- French and British, living mainly in England until 1987.

On 08/05/22 20:45, Athel Cornish-Bowden wrote:
> On 2022-05-08 01:54:00 +0000, hongy...@gmail.com said:
>
>> See the following description here [1]:
>>
>> ``` In mathematics, a module is a generalization of the notion of
>> vector space, wherein the field of scalars is replaced by a ring.
>> The concept of module is also a generalization of the one of
>> abelian group, since the abelian groups are exactly the modules
>> over the ring of integers.``` In the above narration, is the "a
>> generalization of the one of abelian group" a good style?
>
> No. It's almost unintelligible.
>>
>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)
>
> I've changed "one" to "notion", as suggested by CDB.

I would prefer "concept". Otherwise, some people will be left wondering
what the difference is between a concept and a notion.

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

On 2022-05-08 10:55:58 +0000, Peter Moylan said:

> On 08/05/22 20:45, Athel Cornish-Bowden wrote:
>> On 2022-05-08 01:54:00 +0000, hongy...@gmail.com said:
>>
>>> See the following description here [1]:
>>>
>>> ``` In mathematics, a module is a generalization of the notion of
>>> vector space, wherein the field of scalars is replaced by a ring.
>>> The concept of module is also a generalization of the one of
>>> abelian group, since the abelian groups are exactly the modules
>>> over the ring of integers.``` In the above narration, is the "a
>>> generalization of the one of abelian group" a good style?
>>
>> No. It's almost unintelligible.
>>>
>>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)
>>
>> I've changed "one" to "notion", as suggested by CDB.
>
> I would prefer "concept". Otherwise, some people will be left wondering
> what the difference is between a concept and a notion.

I wondered that myself. But I thought it was the same sort of notion as
mentioned already.

--
Athel -- French and British, living mainly in England until 1987.

In message <jdplarFomf5U1@mid.individual.net> Athel Cornish-Bowden <acornish@imm.cnrs.fr> wrote:
> On 2022-05-08 01:54:00 +0000, hongy...@gmail.com said:

>> See the following description here [1]:
>>
>> ```
>> In mathematics, a module is a generalization of the notion of vector
>> space, wherein the field of scalars is replaced by a ring. The concept
>> of module is also a generalization of the one of abelian group, since
>> the abelian groups are exactly the modules over the ring of integers.```
>> In the above narration, is the "a generalization of the one of abelian
>> group" a good style?

> No. It's almost unintelligible.
>>
>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)

> I've changed "one" to "notion", as suggested by CDB.

Notion is a word I tend to avoid, especially in anything having to do
with science, factual information, or related topics. For me, notion has
a sort of wishy-washy quality to it that fits in better with topics like
philosophy, art, drama, poetry. This is because in addition to its
meaning of "concept" it also means "impulse" or "desire".

In the above, concept is the word that I would use, and I would argue
strenuously it is a much better choice.

Reserve 'notion' fro when you are talking about one of many
possibilities, each of which might be perfectly valid.

--
Jamie, would you rather be a lion or a panda?
Coach, I'm me. Why would I want to be anyone else?
I'm not sure you realize how psychologically healthy that is.

On 5/8/2022 6:55 AM, Peter Moylan wrote:
> Athel Cornish-Bowden wrote:
>> hongy...@gmail.com said:

>>> See the following description here [1]:

>>> ``` In mathematics, a module is a generalization of the notion
>>> of vector space, wherein the field of scalars is replaced by a
>>> ring. The concept of module is also a generalization of the one
>>> of abelian group, since the abelian groups are exactly the
>>> modules over the ring of integers.``` In the above narration, is
>>> the "a generalization of the one of abelian group" a good style?

>> No. It's almost unintelligible.

>>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)

>> I've changed "one" to "notion", as suggested by CDB.

> I would prefer "concept". Otherwise, some people will be left
> wondering what the difference is between a concept and a notion.

I think you're right. Clearer is better.

--
I did say "if".

On Sun, 8 May 2022 06:37:28 -0400, CDB <bellemarecd@gmail.com> wrote:

>On 5/7/2022 9:54 PM, hongy...@gmail.com wrote:
>> See the following description here [1]:
>
>> ``` In mathematics, a module is a generalization of the notion of
>> vector space, wherein the field of scalars is replaced by a ring.
>> The concept of module is also a generalization of the one of abelian
>> group, since the abelian groups are exactly the modules over the
>> ring of integers. ``` In the above narration, is the "a
>> generalization of the one of abelian group" a good style?
>
>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)
>
>No. It is also unclear, which is worse.
>
>If the word "one" is intended to stand for "notion",

It probably is, but as you say, it's not clear.

> the word
>"notion" should be used there.

Yes. That would be much better.

>

After serious thinking Ken Blake wrote :
> On Sun, 8 May 2022 06:37:28 -0400, CDB <bellemarecd@gmail.com> wrote:
>
>> On 5/7/2022 9:54 PM, hongy...@gmail.com wrote:
>>> See the following description here [1]:
>>> ``` In mathematics, a module is a generalization of the notion of
>>> vector space, wherein the field of scalars is replaced by a ring.
>>> The concept of module is also a generalization of the one of abelian
>>> group, since the abelian groups are exactly the modules over the
>>> ring of integers. ``` In the above narration, is the "a
>>> generalization of the one of abelian group" a good style?
>>> [1] https://en.wikipedia.org/wiki/Module_(mathematics)
>>
>> No. It is also unclear, which is worse.
>>
>> If the word "one" is intended to stand for "notion",
>
> It probably is, but as you say, it's not clear.

A bit rough, but not unclear.

>> the word
>> "notion" should be used there.
>
>
> Yes. That would be much better.

Oh, please. "Concept". I see that the quote has both "notion" and
"concept", but the latter is better.

/dps

--
Trust, but verify.

On Sunday, May 8, 2022 at 8:38:50 PM UTC+8, Lewis wrote:
> In message <jdplar...@mid.individual.net> Athel Cornish-Bowden <acor...@imm.cnrs.fr> wrote:
> > On 2022-05-08 01:54:00 +0000, hongy...@gmail.com said:
>
> >> See the following description here [1]:
> >>
> >> ```
> >> In mathematics, a module is a generalization of the notion of vector
> >> space, wherein the field of scalars is replaced by a ring. The concept
> >> of module is also a generalization of the one of abelian group, since
> >> the abelian groups are exactly the modules over the ring of integers.```
> >> In the above narration, is the "a generalization of the one of abelian
> >> group" a good style?
>
> > No. It's almost unintelligible.
> >>
> >> [1] https://en.wikipedia.org/wiki/Module_(mathematics)
>
> > I've changed "one" to "notion", as suggested by CDB.
> Notion is a word I tend to avoid, especially in anything having to do
> with science, factual information, or related topics. For me, notion has
> a sort of wishy-washy quality to it that fits in better with topics like
> philosophy, art, drama, poetry. This is because in addition to its
> meaning of "concept" it also means "impulse" or "desire".
>
> In the above, concept is the word that I would use, and I would argue
> strenuously it is a much better choice.
>
> Reserve 'notion' fro when you are talking about one of many

.... for when ...

> possibilities, each of which might be perfectly valid.
>
>
> --
> Jamie, would you rather be a lion or a panda?
> Coach, I'm me. Why would I want to be anyone else?
> I'm not sure you realize how psychologically healthy that is.