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From: porky_pig_jr on 20 Jun 2010 17:58
On Jun 20, 5:40 pm, Frederick Williams <frederick.willia...(a)tesco.net>
wrote:
> Question the first:
>
> I would shorten
>
>     a, b, c, d, e, f, g
>
> to
>
>     a, b, ..., g
>
> but I also see
>
>     a, b, ... g.
>
> Is one right and the other wrong, or is it a matter of taste?  (I think
> I may be tempted to change to the second.)
>

I saw the first the most often. In fact I can't recall if I ever saw
the second. My guess is first is the most common.

BTW, I do hate first, because when I typeset it (with LaTeX), there is
no extra space between \dots and comma. So I usually insert a tiny bit
of space in between.

$a, b, \dots \, , g$.


> Question the second:
>
> I write
>
>     A_{n,m}
>
> but often see
>
>     A_{nm}.
>
> Is one right and the other wrong, or is it a matter of taste?
>
> What I don't like about A_{nm} is that if n and m are numerals one often
> needs a comma: A_{1,11} generally isn't A_{11,1}.
>

Yes, I saw them both and also thought of that as well. Seems like
$A_{nm}$ is OK as long you can keep things clear and unambiguous. It
also often looks cleaner than $A_{n,m}$. But $A_{n,m}$ is more
flexible. I guess I would use $A_{nm}$ if I'm absolutely confident
both $n$ and $m$ will be a single letter and never a digit (or
digits). Other than that, either should be OK.


> --
> I can't go on, I'll go on.

From: Arturo Magidin on 20 Jun 2010 18:38
On Jun 20, 4:40 pm, Frederick Williams <frederick.willia...(a)tesco.net>
wrote:
> Question the first:
>
> I would shorten
>
>     a, b, c, d, e, f, g
>
> to
>
>     a, b, ..., g
>
> but I also see
>
>     a, b, ... g.
>
> Is one right and the other wrong, or is it a matter of taste?  (I think
> I may be tempted to change to the second.)

According to the Chicago Manual of Style, Chapter 13 (Mathematics in
Type), section 13.23:

"13.23: In elisions, if commas or operational signs are required they
should come after each term and after the three ellipsis dots if a
final term follows them. For example:

x_1, x_2, ..., x_n not x_1, x_2, ... x_n
x_1 + x_2 + ... + x_n not x_1 + x_2 + ... x_n
[note: the ellipsis here is mid-level, at the same height as the
-]

y = 0, 1, 2, ... not y = 0, 1, 2 ...

"In the second example above note the centered ellipsis dots have been
used between operational signs, for appearance' sake. Centered dots
may also be used in an expression like

a_1a_2 ... a_n [dots are raised]

for the same reason. It is never incorrect to use on-the-line ellipsis
dots, however, and they are always used in nonmathematical text."

So: First one is correct; second is not.

> Question the second:
>
> I write
>
>     A_{n,m}
>
> but often see
>
>     A_{nm}.
>
> Is one right and the other wrong, or is it a matter of taste?
>
> What I don't like about A_{nm} is that if n and m are numerals one often
> needs a comma: A_{1,11} generally isn't A_{11,1}.

If confusion may arise without the comma, but cannot arise with the
comma, then absolutely put the comma in!

Usually, putting the comma in creates crowded, unpleasant-looking
symbols that do not add to clarity. If one uses n and m as variables,
A_{nm} is unlikely to cause any confusion, and is much easier on the
eye than A_{n,m}. But when the indices may consist of more than one
numeral/symbol, then the comma is necessary to avoid confusion.
Avoiding confusion is always the first and foremost goal, with
pleasant-looking expressions a subsidiary goal.

--
Arturo Magidin
From: achille on 20 Jun 2010 23:04
On Jun 21, 6:38 am, Arturo Magidin <magi...(a)member.ams.org> wrote:
> On Jun 20, 4:40 pm, Frederick Williams <frederick.willia...(a)tesco.net>
> wrote:
>
>
>
> > Question the first:
>
> > I would shorten
>
> >     a, b, c, d, e, f, g
>
> > to
>
> >     a, b, ..., g
>
> > but I also see
>
> >     a, b, ... g.
>
> > Is one right and the other wrong, or is it a matter of taste?  (I think
> > I may be tempted to change to the second.)
>
> According to the Chicago Manual of Style, Chapter 13 (Mathematics in
> Type), section 13.23:
>
> "13.23: In elisions, if commas or operational signs are required they
> should come after each term and after the three ellipsis dots if a
> final term follows them. For example:
>
>    x_1, x_2, ..., x_n          not     x_1, x_2, ... x_n
>    x_1 + x_2 + ... + x_n    not     x_1 + x_2 + ... x_n
>     [note: the ellipsis here is mid-level, at the same height as the
> -]
>
>    y = 0, 1, 2, ...               not       y = 0, 1, 2 ...
>
> "In the second example above note the centered ellipsis dots have been
> used between operational signs, for appearance' sake. Centered dots
> may also be used in an expression like
>
>     a_1a_2 ... a_n    [dots are raised]
>
> for the same reason. It is never incorrect to use on-the-line ellipsis
> dots, however, and they are always used in nonmathematical text."
>
> So: First one is correct; second is not.
>
> > Question the second:
>
> > I write
>
> >     A_{n,m}
>
> > but often see
>
> >     A_{nm}.
>
> > Is one right and the other wrong, or is it a matter of taste?
>
> > What I don't like about A_{nm} is that if n and m are numerals one often
> > needs a comma: A_{1,11} generally isn't A_{11,1}.
>
> If confusion may arise without the comma, but cannot arise with the
> comma, then absolutely put the comma in!
>
> Usually, putting the comma in creates crowded, unpleasant-looking
> symbols that do not add to clarity. If one uses n and m as variables,
> A_{nm} is unlikely to cause any confusion, and is much easier on the
> eye than A_{n,m}. But when the indices may consist of more than one
> numeral/symbol, then the comma is necessary to avoid confusion.
> Avoiding confusion is always the first and foremost goal, with
> pleasant-looking expressions a subsidiary goal.
>
> --
> Arturo Magidin

Actually, in some branches of physics, the comma in
subscript does have meaning. For example, in general
relativity: A_{m,n} usually mean the 'oridinary'
partial derivative of a rank-1 tensor A_m in the
'n'-direction while A_{m n} is a rank-2 tensor.

say general relativity, the comma does mean
In some branches of physics, the comma in the
subscript does mean
A_{m,n} and A_{mn} can mean different thing.
From: Frederick Williams on 21 Jun 2010 05:56
Arturo Magidin wrote:
>
> On Jun 20, 4:40 pm, Frederick Williams <frederick.willia...(a)tesco.net>
> wrote:
> > Question the first:
> >
> > I would shorten
> >
> > a, b, c, d, e, f, g
> >
> > to
> >
> > a, b, ..., g
> >
> > but I also see
> >
> > a, b, ... g.
> >
> > Is one right and the other wrong, or is it a matter of taste? (I think
> > I may be tempted to change to the second.)
>
> According to the Chicago Manual of Style, Chapter 13 (Mathematics in
> Type), section 13.23:
>
> "13.23: In elisions, if commas or operational signs are required they
> should come after each term and after the three ellipsis dots if a
> final term follows them. For example:
>
> x_1, x_2, ..., x_n not x_1, x_2, ... x_n
> x_1 + x_2 + ... + x_n not x_1 + x_2 + ... x_n
> [note: the ellipsis here is mid-level, at the same height as the
> -]
>
> y = 0, 1, 2, ... not y = 0, 1, 2 ...
>
> "In the second example above note the centered ellipsis dots have been
> used between operational signs, for appearance' sake. Centered dots
> may also be used in an expression like
>
> a_1a_2 ... a_n [dots are raised]
>
> for the same reason. It is never incorrect to use on-the-line ellipsis
> dots, however, and they are always used in nonmathematical text."
>
> So: First one is correct; second is not.

Thank you (and, indeed, the Chicago Manual of Style). It is also useful
to have a definitive statement about whether dots are on the line or
raised; I raise them for products but not for lists. This, too, I have
wondered about.

> > Question the second:
> >
> > I write
> >
> > A_{n,m}
> >
> > but often see
> >
> > A_{nm}.
> >
> > Is one right and the other wrong, or is it a matter of taste?
> >
> > What I don't like about A_{nm} is that if n and m are numerals one often
> > needs a comma: A_{1,11} generally isn't A_{11,1}.
>
> If confusion may arise without the comma, but cannot arise with the
> comma, then absolutely put the comma in!
>
> Usually, putting the comma in creates crowded, unpleasant-looking
> symbols that do not add to clarity. If one uses n and m as variables,
> A_{nm} is unlikely to cause any confusion, and is much easier on the
> eye than A_{n,m}. But when the indices may consist of more than one
> numeral/symbol, then the comma is necessary to avoid confusion.
> Avoiding confusion is always the first and foremost goal, with
> pleasant-looking expressions a subsidiary goal.

I suppose I think that if a comma is going to be used sometimes then it
should be used always; at least if it is the same thing being
subscripted.

None of it matters, I'm only compiling notes for my own use, but it's
nice to make things look... um... nice, and nicer still to know one is
doing what the pros do.

--
I can't go on, I'll go on.
From: Frederick Williams on 21 Jun 2010 06:24
achille wrote:
>
> On Jun 21, 6:38 am, Arturo Magidin <magi...(a)member.ams.org> wrote:
> [...]
> >
> > Usually, putting the comma in creates crowded, unpleasant-looking
> > symbols that do not add to clarity. If one uses n and m as variables,
> > A_{nm} is unlikely to cause any confusion, and is much easier on the
> > eye than A_{n,m}. But when the indices may consist of more than one
> > numeral/symbol, then the comma is necessary to avoid confusion.
> > Avoiding confusion is always the first and foremost goal, with
> > pleasant-looking expressions a subsidiary goal.
> >
> > --
> > Arturo Magidin
>
> Actually, in some branches of physics, the comma in
> subscript does have meaning. For example, in general
> relativity: A_{m,n} usually mean the 'oridinary'
> partial derivative of a rank-1 tensor A_m in the
> 'n'-direction while A_{m n} is a rank-2 tensor.

Good thinking! I have seen such things but never written them.

But already one has things like f_{,1,2} for the partial derivative
w.r.t. the second variable of the partial derivative w.r.t. the first
variable of f. I seem to recall that Protter and Morrey prefer this
notation.

--
I can't go on, I'll go on.
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