Why would one number theorems, propositions and lemmas separately?Should one use “above” and “below” in mathematical writing?Examples and importance of Embedding (and Non-Embedding) TheoremsWhy should one still teach Riemann integration?Two different theorems but only one fact?13 months and not even one report. what would you do?What are good ways to present proofs of theorems requiring auxiliary lemmas?What are some deep theorems, and why are they considered deep?What is the correct preposition? (And is there one?)Why should one subscribe to print JournalsWould mathematics be different if not written one-dimensionally?
Why would one number theorems, propositions and lemmas separately?
Should one use “above” and “below” in mathematical writing?Examples and importance of Embedding (and Non-Embedding) TheoremsWhy should one still teach Riemann integration?Two different theorems but only one fact?13 months and not even one report. what would you do?What are good ways to present proofs of theorems requiring auxiliary lemmas?What are some deep theorems, and why are they considered deep?What is the correct preposition? (And is there one?)Why should one subscribe to print JournalsWould mathematics be different if not written one-dimensionally?
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When it comes to numbering results in a mathematical publication, I'm aware of two methods:
Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc.
Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1, etc.
Every piece of writting advice I have encountered advocates the use of 1. over 2., the rationale being that it makes it easier to find the result based on the number. It seems that 1. is more popular than 2., although 2. still exists, especially in books. I can only imagine that people using 2. must have a reason, but I have not yet to encounter one. I hope it is not too opinion-based to ask:
What is the rationale for separately numbering theorems, propositions and lemmas, like in 2.?"
soft-question mathematical-writing
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add a comment |
$begingroup$
When it comes to numbering results in a mathematical publication, I'm aware of two methods:
Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc.
Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1, etc.
Every piece of writting advice I have encountered advocates the use of 1. over 2., the rationale being that it makes it easier to find the result based on the number. It seems that 1. is more popular than 2., although 2. still exists, especially in books. I can only imagine that people using 2. must have a reason, but I have not yet to encounter one. I hope it is not too opinion-based to ask:
What is the rationale for separately numbering theorems, propositions and lemmas, like in 2.?"
soft-question mathematical-writing
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2
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
2
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
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I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago
add a comment |
$begingroup$
When it comes to numbering results in a mathematical publication, I'm aware of two methods:
Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc.
Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1, etc.
Every piece of writting advice I have encountered advocates the use of 1. over 2., the rationale being that it makes it easier to find the result based on the number. It seems that 1. is more popular than 2., although 2. still exists, especially in books. I can only imagine that people using 2. must have a reason, but I have not yet to encounter one. I hope it is not too opinion-based to ask:
What is the rationale for separately numbering theorems, propositions and lemmas, like in 2.?"
soft-question mathematical-writing
$endgroup$
When it comes to numbering results in a mathematical publication, I'm aware of two methods:
Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc.
Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1, etc.
Every piece of writting advice I have encountered advocates the use of 1. over 2., the rationale being that it makes it easier to find the result based on the number. It seems that 1. is more popular than 2., although 2. still exists, especially in books. I can only imagine that people using 2. must have a reason, but I have not yet to encounter one. I hope it is not too opinion-based to ask:
What is the rationale for separately numbering theorems, propositions and lemmas, like in 2.?"
soft-question mathematical-writing
soft-question mathematical-writing
asked 8 hours ago
community wiki
Jakub Konieczny
2
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
2
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
$begingroup$
I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago
add a comment |
2
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
2
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
$begingroup$
I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago
2
2
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
2
2
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
$begingroup$
I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago
add a comment |
1 Answer
1
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oldest
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$begingroup$
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis, in Theorem 3 we will have to employ some Ramsey theory.
$endgroup$
add a comment |
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$begingroup$
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis, in Theorem 3 we will have to employ some Ramsey theory.
$endgroup$
add a comment |
$begingroup$
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis, in Theorem 3 we will have to employ some Ramsey theory.
$endgroup$
add a comment |
$begingroup$
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis, in Theorem 3 we will have to employ some Ramsey theory.
$endgroup$
If the paper contains three main theorems, each generalizing the previous, it is nice to be able to discuss them like this:
While the extension of Theorem 1 to Theorem 2 uses only complex analysis, in Theorem 3 we will have to employ some Ramsey theory.
answered 8 hours ago
community wiki
Bjørn Kjos-Hanssen
add a comment |
add a comment |
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2
$begingroup$
The reader may quickly count the theorems in your paper.
$endgroup$
– Fedor Petrov
8 hours ago
2
$begingroup$
If a short paper has three main results, the second of which has a long proof with five lemmas, then Thm. 1, Thm. 2, Lem. 1-5, Thm. 3 makes total sense.
$endgroup$
– François G. Dorais♦
8 hours ago
$begingroup$
I have always assumed that most people using method 2 haven't really thought about it and are just letting LaTeX get away with its default behavior. To make LaTeX use method 1 you have to explicitly tell it to use the same counter for all results.
$endgroup$
– Mike Shulman
7 hours ago
$begingroup$
@MikeShulman Most people in the present day, for sure. But it's also used (annoyingly) in some pre-LaTeX textbooks, such as Berberian's Baer *-rings.
$endgroup$
– Robert Furber
36 mins ago