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"by an abuse of notation" vs. "by abuse of notation"
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jaakov
Apr 30, 2015, 9:15:14 AM4/30/15
to
Dear all:
Which one is correct and why:
- By an abuse of notation, we use the same symbol here as in Section 1.
- By abuse of notation, we use the same symbol here as in Section 1.
Thank you in advance,
Jaakov.
Which one is correct and why:
- By an abuse of notation, we use the same symbol here as in Section 1.
- By abuse of notation, we use the same symbol here as in Section 1.
Thank you in advance,
Jaakov.
Anton Shepelev
Apr 30, 2015, 9:35:53 AM4/30/15
to
jaakov:
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
I should say neither is, for abuse of notation is
not a way to denote two different things with the
same symbol. How about:
By using the symbol here as in Section 1, we are
abusing notation.
As to the indefinite article, I thing it should be
omitted.
--
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/\ http://preview.tinyurl.com/qcy6mjc [archived]
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
not a way to denote two different things with the
same symbol. How about:
By using the symbol here as in Section 1, we are
abusing notation.
As to the indefinite article, I thing it should be
omitted.
--
() ascii ribbon campaign - against html e-mail
/\ http://preview.tinyurl.com/qcy6mjc [archived]
Anton Shepelev
Apr 30, 2015, 9:37:28 AM4/30/15
to
I wrote:
> By using the symbol here as in Section 1, we are
> abusing notation.
meaning: "by using the same symbol here as in..."
> By using the symbol here as in Section 1, we are
> abusing notation.
Don Phillipson
Apr 30, 2015, 9:40:33 AM4/30/15
to
"jaakov" <jaakovR...@DELETEITro.ru> wrote in message
news:mht9su$cfr$9...@speranza.aioe.org...
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
Multiple answers are possible because no context is indicated
although several are implied.
The sentence includes two different statements:
-- factual description, that this notation is the same as in Sec. 1
-- value judgment, that this notation is abusive.
We are not obliged to combine these two in a single sentence:
and some authors prefer not to. We can justify our preferences,
but no rules oblige us to think uniformly.
--
Don Phillipson
Carlsbad Springs
(Ottawa, Canada)
news:mht9su$cfr$9...@speranza.aioe.org...
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
although several are implied.
The sentence includes two different statements:
-- factual description, that this notation is the same as in Sec. 1
-- value judgment, that this notation is abusive.
We are not obliged to combine these two in a single sentence:
and some authors prefer not to. We can justify our preferences,
but no rules oblige us to think uniformly.
--
Don Phillipson
Carlsbad Springs
(Ottawa, Canada)
jaakov
Apr 30, 2015, 10:05:58 AM4/30/15
to
In section 1, we defined 3-adic relation [right arrow]
x [right arrow]^a y :<=> ... .
In Section 2, we introduce another relation, a 4-adic one, which is
related to the previous 3-adic one:
x [right arrow]^w_i y :<=> ... .
Essentially, the 4-adic one is a relation on words w of length i, which
extends the 3-adic one, which is relation on symbols a (i.e. words of
length 1).
I wish to make the reader aware of the following facts in the most
compact and understandable way:
Logically speaking, these relations are different. But they are
intuitively similar, so that we decide to use the same symbol for them.
"By (an) abuse of (the) notation, we use here the same symbol as in
Section 1."
Anton Shepelev
Apr 30, 2015, 10:30:52 AM4/30/15
to
jaakov:
> Here is the context.
>
> In section 1, we defined 3-adic relation [right
> arrow]
>
> x [right arrow]^a y :<=> ... .
>
> In Section 2, we introduce another relation, a
> 4-adic one, which is related to the previous
> 3-adic one:
>
> x [right arrow]^w_i y :<=> ... .
>
> Essentially, the 4-adic one is a relation on words
> w of length i, which extends the 3-adic one, which
> is relation on symbols a (i.e. words of length 1).
I should avoid all confusion by employing an unam-
biguous notation, e.g.:
R0( x, a, y ) = ...
R1( x, w, i, y ) = R0( x, w_i, y )
> Here is the context.
>
> In section 1, we defined 3-adic relation [right
> arrow]
>
> x [right arrow]^a y :<=> ... .
>
> In Section 2, we introduce another relation, a
> 4-adic one, which is related to the previous
> 3-adic one:
>
> x [right arrow]^w_i y :<=> ... .
>
> Essentially, the 4-adic one is a relation on words
> w of length i, which extends the 3-adic one, which
> is relation on symbols a (i.e. words of length 1).
biguous notation, e.g.:
R0( x, a, y ) = ...
R1( x, w, i, y ) = R0( x, w_i, y )
jaakov
Apr 30, 2015, 11:06:15 AM4/30/15
to
Am 30.04.2015 um 16:30 schrieb Anton Shepelev:
> jaakov:
>
>> Here is the context.
>>
>> In section 1, we defined 3-adic relation [right
>> arrow]
>>
>> x [right arrow]^a y :<=> ... .
>>
>> In Section 2, we introduce another relation, a
>> 4-adic one, which is related to the previous
>> 3-adic one:
>>
>> x [right arrow]^w_i y :<=> ... .
>>
>> Essentially, the 4-adic one is a relation on words
>> w of length i, which extends the 3-adic one, which
>> is relation on symbols a (i.e. words of length 1).
>
> I should avoid all confusion by employing an unam-
> biguous notation, e.g.:
>
> R0( x, a, y ) = ...
> R1( x, w, i, y ) = R0( x, w_i, y )
>
Please don't change the question.
> jaakov:
>
>> Here is the context.
>>
>> In section 1, we defined 3-adic relation [right
>> arrow]
>>
>> x [right arrow]^a y :<=> ... .
>>
>> In Section 2, we introduce another relation, a
>> 4-adic one, which is related to the previous
>> 3-adic one:
>>
>> x [right arrow]^w_i y :<=> ... .
>>
>> Essentially, the 4-adic one is a relation on words
>> w of length i, which extends the 3-adic one, which
>> is relation on symbols a (i.e. words of length 1).
>
> I should avoid all confusion by employing an unam-
> biguous notation, e.g.:
>
> R0( x, a, y ) = ...
> R1( x, w, i, y ) = R0( x, w_i, y )
>
(PS. I have used R with an index already for other things. Abusing
notation may be wrong, but it also may be the right thing to do in
certain circumstances. E.g., when speaking about graphs with labeled
edges, arrows with an upper index may represent both labels of arcs and
labels of walks. In my text, I have a similar situation. So please just
take the above setup.)
Daniel James
May 1, 2015, 1:48:23 PM5/1/15
to
In article <mht9su$cfr$9...@speranza.aioe.org>, Jaakov wrote:
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
If it's something you're doing once then "by an abuse" seems more
> Which one is correct and why:
>
> - By an abuse of notation, we use the same symbol here as in Section 1.
> - By abuse of notation, we use the same symbol here as in Section 1.
natural to me, but if it's something that you do repeatedly or as
a matter of practice than "by abuse" is better.
Given the context you present downthread I'd say that "by abuse"
is what you want.
--
Cheers,
Daniel.
Anton Shepelev
May 1, 2015, 3:05:57 PM5/1/15
to
jaakov:
> > > ing facts in the most compact and understand-
> > ambiguous notation, e.g.:
> > [...]
ter, 4-adic, relation on words. This change is ad-
missible, for we shan't need the 3-adic relation on
symbols anymore, and convenient, for the new rela-
tion is a natural extension of the old.
But I am still at a loss as to the way you turn a
relation on symbols into one on symbol sequences of
fixed length, and the way you demostrate it using
the same symbol for both relations...
> Anton Shepelev:
> > jaakov:
> >
> > > Here is the context.
> > >
> > > In section 1, we defined 3-adic relation
> > > [right arrow]
> > >
> > > x [right arrow]^a y :<=> ... .
> > >
> > > In Section 2, we introduce another relation, a
> > > 4-adic one, which is related to the previous
> > > 3-adic one:
> > >
> > > x [right arrow]^w_i y :<=> ... .
> > >
> > > Essentially, the 4-adic one is a relation on
> > > words w of length i, which extends the 3-adic
> > > one, which is relation on symbols a (i.e.
> > > words of length 1).
> > >
> > > I wish to make the reader aware of the follow-
> > jaakov:
> >
> > > Here is the context.
> > >
> > > In section 1, we defined 3-adic relation
> > > [right arrow]
> > >
> > > x [right arrow]^a y :<=> ... .
> > >
> > > In Section 2, we introduce another relation, a
> > > 4-adic one, which is related to the previous
> > > 3-adic one:
> > >
> > > x [right arrow]^w_i y :<=> ... .
> > >
> > > Essentially, the 4-adic one is a relation on
> > > words w of length i, which extends the 3-adic
> > > one, which is relation on symbols a (i.e.
> > > words of length 1).
> > >
> > > ing facts in the most compact and understand-
> > > able way: Logically speaking, these relations
> > > are different. But they are intuitively simi-
> > > lar, so that we decide to use the same symbol
> > > for them.
> >
> > I should avoid all confusion by employing an un-
> > > for them.
> >
> > ambiguous notation, e.g.:
> > [...]
>
> Please don't change the question.
[such and such notation] will now refer to the lat-
> Please don't change the question.
ter, 4-adic, relation on words. This change is ad-
missible, for we shan't need the 3-adic relation on
symbols anymore, and convenient, for the new rela-
tion is a natural extension of the old.
But I am still at a loss as to the way you turn a
relation on symbols into one on symbol sequences of
fixed length, and the way you demostrate it using
the same symbol for both relations...
Jaakov
May 1, 2015, 4:35:59 PM5/1/15
to
then this question might be not the one you can address anyway...
Example: Look at the acceptance of words by regular finite automata.
Letters take you from states to states in one step. Finite words take
you also from states to states (in zero, one, or many steps). We use one
and the same symbol (arrow) for both relations.
Peter Moylan
May 1, 2015, 11:23:18 PM5/1/15
to
On 02/05/15 06:35, Jaakov wrote:
> Let me ask you: are you doing maths in English on a daily basis? If not,
> then this question might be not the one you can address anyway...
>
> Example: Look at the acceptance of words by regular finite automata.
> Letters take you from states to states in one step. Finite words take
> you also from states to states (in zero, one, or many steps). We use one
> and the same symbol (arrow) for both relations.
That must be an innovation since I studied automata theory. (Which was,
> Let me ask you: are you doing maths in English on a daily basis? If not,
> then this question might be not the one you can address anyway...
>
> Example: Look at the acceptance of words by regular finite automata.
> Letters take you from states to states in one step. Finite words take
> you also from states to states (in zero, one, or many steps). We use one
> and the same symbol (arrow) for both relations.
admittedly, years ago.) As I recall it, a superscript star applied to
any dyadic operator meant "reflexive transitive completion". Thus, you
used an arrow for a single step, but an arrow with a star above it to
mean "zero or more steps".
--
Peter Moylan http://www.pmoylan.org
Newcastle, NSW, Australia
alien8er
May 1, 2015, 11:38:19 PM5/1/15
to
On Thursday, April 30, 2015 at 7:05:58 AM UTC-7, Jaakov wrote:
> Am 30.04.2015 um 15:40 schrieb Don Phillipson:
> > "jaakov" <jaakovR...@DELETEITro.ru> wrote in message
> > news:mht9su$cfr$9...@speranza.aioe.org...
> >
> >> Which one is correct and why:
> >>
> >> - By an abuse of notation, we use the same symbol here as in Section 1.
> >> - By abuse of notation, we use the same symbol here as in Section 1.
> >
> > Multiple answers are possible because no context is indicated
> > although several are implied.
> >
> > The sentence includes two different statements:
> > -- factual description, that this notation is the same as in Sec. 1
> > -- value judgment, that this notation is abusive.
> > We are not obliged to combine these two in a single sentence:
> > and some authors prefer not to. We can justify our preferences,
> > but no rules oblige us to think uniformly.
> >
> Here is the context.
>
> In section 1, we defined 3-adic relation [right arrow]
>
> x [right arrow]^a y :<=> ... .
>
> In Section 2, we introduce another relation, a 4-adic one, which is
> related to the previous 3-adic one:
>
> x [right arrow]^w_i y :<=> ... .
>
> Essentially, the 4-adic one is a relation on words w of length i, which
> extends the 3-adic one, which is relation on symbols a (i.e. words of
> length 1).
Is there no existing standardized notation? If there is, why aren't you using it?
> Am 30.04.2015 um 15:40 schrieb Don Phillipson:
> > "jaakov" <jaakovR...@DELETEITro.ru> wrote in message
> > news:mht9su$cfr$9...@speranza.aioe.org...
> >
> >> Which one is correct and why:
> >>
> >> - By an abuse of notation, we use the same symbol here as in Section 1.
> >> - By abuse of notation, we use the same symbol here as in Section 1.
> >
> > Multiple answers are possible because no context is indicated
> > although several are implied.
> >
> > The sentence includes two different statements:
> > -- factual description, that this notation is the same as in Sec. 1
> > -- value judgment, that this notation is abusive.
> > We are not obliged to combine these two in a single sentence:
> > and some authors prefer not to. We can justify our preferences,
> > but no rules oblige us to think uniformly.
> >
> Here is the context.
>
> In section 1, we defined 3-adic relation [right arrow]
>
> x [right arrow]^a y :<=> ... .
>
> In Section 2, we introduce another relation, a 4-adic one, which is
> related to the previous 3-adic one:
>
> x [right arrow]^w_i y :<=> ... .
>
> Essentially, the 4-adic one is a relation on words w of length i, which
> extends the 3-adic one, which is relation on symbols a (i.e. words of
> length 1).
> I wish to make the reader aware of the following facts in the most
> compact and understandable way:
[(possibly) A. Einstein]
> Logically speaking, these relations are different. But they are
> intuitively similar, so that we decide to use the same symbol for them.
> "By (an) abuse of (the) notation, we use here the same symbol as in
> Section 1."
"Logically speaking, these relations are different in that..."
Ambiguity in English prose is occasionally acceptable (and encouraged in poetry) but not when dealing with mathematics.
Dr. HotSalt
Jaakov
May 1, 2015, 11:51:53 PM5/1/15
to
In my representation, I need to account for the word length explicitly.
This is where the fourth argument i comes into play. My 4-adic relation
uses the right superscript i to denote the length of the word instead of
the right superscript star:
word i
automaton node --------> another node
Jaakov
May 1, 2015, 11:54:25 PM5/1/15
to
> Is there no existing standardized notation?
No.
> If there is, why aren't you using it?
>
>> Logically speaking, these relations are different. But they are
>> intuitively similar, so that we decide to use the same symbol for them.
>
> Then say that rather than the following.
Too long. No way.
>> Logically speaking, these relations are different. But they are
>> intuitively similar, so that we decide to use the same symbol for them.
>
> Then say that rather than the following.
>
>> "By (an) abuse of (the) notation, we use here the same symbol as in
>> Section 1."
>
> It would also help to clarify explicitly what the logical difference is.
>
> "Logically speaking, these relations are different in that..."
>
> Ambiguity in English prose is occasionally acceptable (and encouraged in poetry) but not when dealing with mathematics.
>
>
> Dr. HotSalt
>
Anton Shepelev
May 3, 2015, 9:22:16 AM5/3/15
to
Jaakov:
> In my representation, I need to account for the
> word length explicitly. This is where the fourth
> argument i comes into play. My 4-adic relation
> uses the right superscript i to denote the length
> of the word instead of the right superscript star:
>
> word i
> automaton node --------> another node
I still don't understant. Would you be so kind as
to tell me how this relation can be a 4-adic one?
The length being an inherent property of a word,
this must be a 3-adic relation on:
a. initial node,
b. input word, and
c. final node
Your limiting the set of words to those with length
i cannot make it a 4-adic relation and will only
split the 3-adic relation on all words into several
3-adic relations on words with a fixed length.
> In my representation, I need to account for the
> word length explicitly. This is where the fourth
> argument i comes into play. My 4-adic relation
> uses the right superscript i to denote the length
> of the word instead of the right superscript star:
>
> word i
> automaton node --------> another node
to tell me how this relation can be a 4-adic one?
The length being an inherent property of a word,
this must be a 3-adic relation on:
a. initial node,
b. input word, and
c. final node
Your limiting the set of words to those with length
i cannot make it a 4-adic relation and will only
split the 3-adic relation on all words into several
3-adic relations on words with a fixed length.
Anton Shepelev
May 3, 2015, 9:34:49 AM5/3/15
to
Jaakov to Anton Shepelev:
> > But I am still at a loss as to the way you turn
> > a relation on symbols into one on symbol se-
> > quences of fixed length, and the way you de-
> > mostrate it using the same symbol for both rela-
> If not, then this question might be not the one
> you can address anyway...
>
> Example: Look at the acceptance of words by regu-
a
S_n => S_{n+1}
w i a1 ai
S_n => S_{n+i} or S_n => S_{n+1} => ... => S_{n+i}
There is no abouse here, for the latter transition
is defined as a sequence of elementary transitions.
'=>' denotes a transition between nodes upon read-
ing a sequence of symbols, be it a symbol, a word,
or an empty string.
> > But I am still at a loss as to the way you turn
> > quences of fixed length, and the way you de-
> > mostrate it using the same symbol for both rela-
> > tions...
>
> Let me ask you: are you doing maths in English on
> a daily basis?
No, I amn't.
>
> Let me ask you: are you doing maths in English on
> a daily basis?
> If not, then this question might be not the one
> you can address anyway...
>
> lar finite automata. Letters take you from states
> to states in one step. Finite words take you also
> from states to states (in zero, one, or many
> steps). We use one and the same symbol (arrow)
> for both relations.
I see:
> to states in one step. Finite words take you also
> from states to states (in zero, one, or many
> steps). We use one and the same symbol (arrow)
> for both relations.
a
S_n => S_{n+1}
w i a1 ai
S_n => S_{n+i} or S_n => S_{n+1} => ... => S_{n+i}
There is no abouse here, for the latter transition
is defined as a sequence of elementary transitions.
'=>' denotes a transition between nodes upon read-
ing a sequence of symbols, be it a symbol, a word,
or an empty string.
Jaakov
May 3, 2015, 1:37:01 PM5/3/15
to
On 03.05.2015 15:35, Anton Shepelev wrote:
> Jaakov to Anton Shepelev:
>
>>> But I am still at a loss as to the way you turn
>>> a relation on symbols into one on symbol se-
>>> quences of fixed length, and the way you de-
>>> mostrate it using the same symbol for both rela-
>>> tions...
>>
>> Let me ask you: are you doing maths in English on
>> a daily basis?
>
> No, I amn't.
>
Dear Anton:
> Jaakov to Anton Shepelev:
>
>>> But I am still at a loss as to the way you turn
>>> a relation on symbols into one on symbol se-
>>> quences of fixed length, and the way you de-
>>> mostrate it using the same symbol for both rela-
>>> tions...
>>
>> Let me ask you: are you doing maths in English on
>> a daily basis?
>
> No, I amn't.
>
Then please just forget this conversation; it would be a loss of time
for both of us. I'm sorry for not having clearly stated it upfront.
Best,
Jaakov
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