Problem in Math Writing [closed]
$begingroup$
I have a problem in math writing.
Consider $a_i$ with $1leq i leq n$ are some elements over a field.
My Question: Which of the following statements is correct?
A) Let $a_i$'s satisfy the following condition.
B) Let $a_i$'s satisfies the following condition.
Thanks for your suggestions.
proof-writing article-writing
asked Nov 24 '18 at 20:55
user0410user0410
19410
$endgroup$
closed as off-topic by amWhy, Holo, Rebellos, KReiser, user10354138 Nov 25 '18 at 3:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – amWhy, Holo, Rebellos, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I have a problem in math writing.
Consider $a_i$ with $1leq i leq n$ are some elements over a field.
My Question: Which of the following statements is correct?
A) Let $a_i$'s satisfy the following condition.
B) Let $a_i$'s satisfies the following condition.
Thanks for your suggestions.
proof-writing article-writing
asked Nov 24 '18 at 20:55
user0410user0410
19410
$endgroup$
closed as off-topic by amWhy, Holo, Rebellos, KReiser, user10354138 Nov 25 '18 at 3:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – amWhy, Holo, Rebellos, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
1
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
1
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16
add a comment |
$begingroup$
I have a problem in math writing.
Consider $a_i$ with $1leq i leq n$ are some elements over a field.
My Question: Which of the following statements is correct?
A) Let $a_i$'s satisfy the following condition.
B) Let $a_i$'s satisfies the following condition.
Thanks for your suggestions.
proof-writing article-writing
asked Nov 24 '18 at 20:55
user0410user0410
19410
$endgroup$
I have a problem in math writing.
Consider $a_i$ with $1leq i leq n$ are some elements over a field.
My Question: Which of the following statements is correct?
A) Let $a_i$'s satisfy the following condition.
B) Let $a_i$'s satisfies the following condition.
Thanks for your suggestions.
proof-writing article-writing
proof-writing article-writing
asked Nov 24 '18 at 20:55
user0410user0410
19410
asked Nov 24 '18 at 20:55
user0410user0410
19410
asked Nov 24 '18 at 20:55
user0410user0410
19410
asked Nov 24 '18 at 20:55
user0410user0410
19410
asked Nov 24 '18 at 20:55
user0410user0410
19410
19410
closed as off-topic by amWhy, Holo, Rebellos, KReiser, user10354138 Nov 25 '18 at 3:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – amWhy, Holo, Rebellos, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, Holo, Rebellos, KReiser, user10354138 Nov 25 '18 at 3:03
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." – amWhy, Holo, Rebellos, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
1
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
1
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16
add a comment |
3
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
1
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
1
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16
3
3
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
1
1
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
1
1
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
I might say something like
Suppose the $a_i$ satisfy ...
or
Suppose $n$ field elements ${a_i}$ ( $1 le i le n$ )
satisfy ...
In any case the apostrophy s on $a_i$'s feels wrong to me. You do want the plural "satisfy" since you are talking about a sequence of several elements (plural).
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
$endgroup$
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
add a comment |
$begingroup$
In general, it is inappropriate to use an apostrophe-s to pluralize English nouns. However, the AMS style guide (which seems to be an appropriate style guide, given the context) instructs us to use the apostrophe-s to make variable names plural (see page 94). Hence that part of the construction is appropriate.
That being said, the heart of the question seems to be about the correct conjugation of the verb "to satisfy." The verb should be conjugated in order to agree with the subject of the sentence. In this case, the subject of the sentence is "the $a_i$'s", which demands a third person plural conjugation, i.e.
The $a_i$'s satisfy...
That being said, I agree with Ethan Bolker's assessment that the phrasing is a little awkward, in part because of the apostrophe-s. An equally readable alternative might be
The $a_i$ satisfy...
Personally, I might prefer a phrasing which emphasizes the common properties of the field elements in the set. Hence I would probably write a sentence more like
Let $k$ be a field and let ${a_i}_{i=1}^{N} subseteq k$ be a collection which satisfies the condition...
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
$endgroup$
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I might say something like
Suppose the $a_i$ satisfy ...
or
Suppose $n$ field elements ${a_i}$ ( $1 le i le n$ )
satisfy ...
In any case the apostrophy s on $a_i$'s feels wrong to me. You do want the plural "satisfy" since you are talking about a sequence of several elements (plural).
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
$endgroup$
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
add a comment |
$begingroup$
I might say something like
Suppose the $a_i$ satisfy ...
or
Suppose $n$ field elements ${a_i}$ ( $1 le i le n$ )
satisfy ...
In any case the apostrophy s on $a_i$'s feels wrong to me. You do want the plural "satisfy" since you are talking about a sequence of several elements (plural).
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
$endgroup$
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
add a comment |
$begingroup$
I might say something like
Suppose the $a_i$ satisfy ...
or
Suppose $n$ field elements ${a_i}$ ( $1 le i le n$ )
satisfy ...
In any case the apostrophy s on $a_i$'s feels wrong to me. You do want the plural "satisfy" since you are talking about a sequence of several elements (plural).
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
$endgroup$
I might say something like
Suppose the $a_i$ satisfy ...
or
Suppose $n$ field elements ${a_i}$ ( $1 le i le n$ )
satisfy ...
In any case the apostrophy s on $a_i$'s feels wrong to me. You do want the plural "satisfy" since you are talking about a sequence of several elements (plural).
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
edited Nov 24 '18 at 21:19
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
answered Nov 24 '18 at 21:05
Ethan BolkerEthan Bolker
43.5k551116
43.5k551116
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
add a comment |
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
1
1
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
$begingroup$
I agree that the apostrophe-s feels wrong, but the AMS style guide endorses it.
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:30
add a comment |
$begingroup$
In general, it is inappropriate to use an apostrophe-s to pluralize English nouns. However, the AMS style guide (which seems to be an appropriate style guide, given the context) instructs us to use the apostrophe-s to make variable names plural (see page 94). Hence that part of the construction is appropriate.
That being said, the heart of the question seems to be about the correct conjugation of the verb "to satisfy." The verb should be conjugated in order to agree with the subject of the sentence. In this case, the subject of the sentence is "the $a_i$'s", which demands a third person plural conjugation, i.e.
The $a_i$'s satisfy...
That being said, I agree with Ethan Bolker's assessment that the phrasing is a little awkward, in part because of the apostrophe-s. An equally readable alternative might be
The $a_i$ satisfy...
Personally, I might prefer a phrasing which emphasizes the common properties of the field elements in the set. Hence I would probably write a sentence more like
Let $k$ be a field and let ${a_i}_{i=1}^{N} subseteq k$ be a collection which satisfies the condition...
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
$endgroup$
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
add a comment |
$begingroup$
In general, it is inappropriate to use an apostrophe-s to pluralize English nouns. However, the AMS style guide (which seems to be an appropriate style guide, given the context) instructs us to use the apostrophe-s to make variable names plural (see page 94). Hence that part of the construction is appropriate.
That being said, the heart of the question seems to be about the correct conjugation of the verb "to satisfy." The verb should be conjugated in order to agree with the subject of the sentence. In this case, the subject of the sentence is "the $a_i$'s", which demands a third person plural conjugation, i.e.
The $a_i$'s satisfy...
That being said, I agree with Ethan Bolker's assessment that the phrasing is a little awkward, in part because of the apostrophe-s. An equally readable alternative might be
The $a_i$ satisfy...
Personally, I might prefer a phrasing which emphasizes the common properties of the field elements in the set. Hence I would probably write a sentence more like
Let $k$ be a field and let ${a_i}_{i=1}^{N} subseteq k$ be a collection which satisfies the condition...
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
$endgroup$
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
add a comment |
$begingroup$
In general, it is inappropriate to use an apostrophe-s to pluralize English nouns. However, the AMS style guide (which seems to be an appropriate style guide, given the context) instructs us to use the apostrophe-s to make variable names plural (see page 94). Hence that part of the construction is appropriate.
That being said, the heart of the question seems to be about the correct conjugation of the verb "to satisfy." The verb should be conjugated in order to agree with the subject of the sentence. In this case, the subject of the sentence is "the $a_i$'s", which demands a third person plural conjugation, i.e.
The $a_i$'s satisfy...
That being said, I agree with Ethan Bolker's assessment that the phrasing is a little awkward, in part because of the apostrophe-s. An equally readable alternative might be
The $a_i$ satisfy...
Personally, I might prefer a phrasing which emphasizes the common properties of the field elements in the set. Hence I would probably write a sentence more like
Let $k$ be a field and let ${a_i}_{i=1}^{N} subseteq k$ be a collection which satisfies the condition...
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
$endgroup$
In general, it is inappropriate to use an apostrophe-s to pluralize English nouns. However, the AMS style guide (which seems to be an appropriate style guide, given the context) instructs us to use the apostrophe-s to make variable names plural (see page 94). Hence that part of the construction is appropriate.
That being said, the heart of the question seems to be about the correct conjugation of the verb "to satisfy." The verb should be conjugated in order to agree with the subject of the sentence. In this case, the subject of the sentence is "the $a_i$'s", which demands a third person plural conjugation, i.e.
The $a_i$'s satisfy...
That being said, I agree with Ethan Bolker's assessment that the phrasing is a little awkward, in part because of the apostrophe-s. An equally readable alternative might be
The $a_i$ satisfy...
Personally, I might prefer a phrasing which emphasizes the common properties of the field elements in the set. Hence I would probably write a sentence more like
Let $k$ be a field and let ${a_i}_{i=1}^{N} subseteq k$ be a collection which satisfies the condition...
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
answered Nov 24 '18 at 21:27
Xander HendersonXander Henderson
14.6k103555
14.6k103555
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
add a comment |
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
I like your alternative making the collection of elements an explicit object which you then follow with the singular "satisfies". It does call for more notation, Whether that's a good thing depends on the surrounding context.
$endgroup$
– Ethan Bolker
Nov 24 '18 at 21:32
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
$begingroup$
@EthanBolker Indeed. Context is everything. ;)
$endgroup$
– Xander Henderson
Nov 24 '18 at 21:33
add a comment |
3
$begingroup$
This is moreso an English/grammar issue than anything. Since there are multiple $a_i$'s, you would say "let the $a_i$'s satisfy, much as you would say "let the numbers satisfy."
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:01
$begingroup$
@EeveeTrainer As far as I understand you mean it is better to write "let the numbers $a_i$'s satisfy". am I right?
$endgroup$
– user0410
Nov 24 '18 at 21:05
1
$begingroup$
Well, you could just say "let the $a_i$'s satisfy". The second phrase "let the numbers satisfy" was more just to show an analogous phrasing. Since there are multiple $a_i$'s, in this context, you could treat it as a plural noun, much as you would the words "cats," "dogs," or "numbers," and use the corresponding form of the verb ("satisfy" in this case). Ethan Bolker, in his answer below, also gives a few alternative ways of phrasing it that are equally valid.
$endgroup$
– Eevee Trainer
Nov 24 '18 at 21:13
$begingroup$
@EeveeTrainer Thanks for your useful comment. I got it.
$endgroup$
– user0410
Nov 24 '18 at 21:15
1
$begingroup$
Just to clear this up a little: you can say "Let the $a_i$'s satisfy..." or you can say "Let the numbers $a_i$ satisfy...". You definitely can't say "Let the numbers $a_i$'s satisfy...".
$endgroup$
– TonyK
Nov 24 '18 at 21:16