Notation question: Is there a difference between centered dots and lower dots?
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In mathematical notation, do the "lower dots", i.e. $A, B,ldots , K$ have a different meaning than the "centered dots", i.e. $A, B, cdots, K$?
For instance, is it the case that lower dots are used for, say, sets such as ${A, B, ldots, K }, $ while the centered dots are used for things like multiplication of terms, such as in $Acdot Bcdot cdots cdot K$? Or can they be used interchangeably?
The accepted answer from this question would suggest that they can be used interchangeably, but that lowered dots are typically used after commas, whereas centered dots are used after mathematical operations. However, since I find the lowered dots more aesthetically pleasing, I want to know if it is correct or in stark opposition to notational decency to use the lower dots anyway.
notation
asked Jan 17 at 10:30
PhilPhil
1032
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add a comment |
$begingroup$
In mathematical notation, do the "lower dots", i.e. $A, B,ldots , K$ have a different meaning than the "centered dots", i.e. $A, B, cdots, K$?
For instance, is it the case that lower dots are used for, say, sets such as ${A, B, ldots, K }, $ while the centered dots are used for things like multiplication of terms, such as in $Acdot Bcdot cdots cdot K$? Or can they be used interchangeably?
The accepted answer from this question would suggest that they can be used interchangeably, but that lowered dots are typically used after commas, whereas centered dots are used after mathematical operations. However, since I find the lowered dots more aesthetically pleasing, I want to know if it is correct or in stark opposition to notational decency to use the lower dots anyway.
notation
asked Jan 17 at 10:30
PhilPhil
1032
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$Acdot Bcdot ldots cdot K$ looks strange to me
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– Henry
Jan 17 at 10:43
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In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
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– Rosie F
Jan 17 at 10:48
1
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It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
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– TonyK
Jan 17 at 10:50
add a comment |
$begingroup$
In mathematical notation, do the "lower dots", i.e. $A, B,ldots , K$ have a different meaning than the "centered dots", i.e. $A, B, cdots, K$?
For instance, is it the case that lower dots are used for, say, sets such as ${A, B, ldots, K }, $ while the centered dots are used for things like multiplication of terms, such as in $Acdot Bcdot cdots cdot K$? Or can they be used interchangeably?
The accepted answer from this question would suggest that they can be used interchangeably, but that lowered dots are typically used after commas, whereas centered dots are used after mathematical operations. However, since I find the lowered dots more aesthetically pleasing, I want to know if it is correct or in stark opposition to notational decency to use the lower dots anyway.
notation
asked Jan 17 at 10:30
PhilPhil
1032
$endgroup$
In mathematical notation, do the "lower dots", i.e. $A, B,ldots , K$ have a different meaning than the "centered dots", i.e. $A, B, cdots, K$?
For instance, is it the case that lower dots are used for, say, sets such as ${A, B, ldots, K }, $ while the centered dots are used for things like multiplication of terms, such as in $Acdot Bcdot cdots cdot K$? Or can they be used interchangeably?
The accepted answer from this question would suggest that they can be used interchangeably, but that lowered dots are typically used after commas, whereas centered dots are used after mathematical operations. However, since I find the lowered dots more aesthetically pleasing, I want to know if it is correct or in stark opposition to notational decency to use the lower dots anyway.
notation
notation
asked Jan 17 at 10:30
PhilPhil
1032
asked Jan 17 at 10:30
PhilPhil
1032
asked Jan 17 at 10:30
PhilPhil
1032
asked Jan 17 at 10:30
PhilPhil
1032
asked Jan 17 at 10:30
PhilPhil
1032
1032
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$Acdot Bcdot ldots cdot K$ looks strange to me
$endgroup$
– Henry
Jan 17 at 10:43
$begingroup$
In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
$endgroup$
– Rosie F
Jan 17 at 10:48
1
$begingroup$
It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
$endgroup$
– TonyK
Jan 17 at 10:50
add a comment |
$begingroup$
$Acdot Bcdot ldots cdot K$ looks strange to me
$endgroup$
– Henry
Jan 17 at 10:43
$begingroup$
In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
$endgroup$
– Rosie F
Jan 17 at 10:48
1
$begingroup$
It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
$endgroup$
– TonyK
Jan 17 at 10:50
$begingroup$
$Acdot Bcdot ldots cdot K$ looks strange to me
$endgroup$
– Henry
Jan 17 at 10:43
$begingroup$
$Acdot Bcdot ldots cdot K$ looks strange to me
$endgroup$
– Henry
Jan 17 at 10:43
$begingroup$
In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
$endgroup$
– Rosie F
Jan 17 at 10:48
$begingroup$
In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
$endgroup$
– Rosie F
Jan 17 at 10:48
1
1
$begingroup$
It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
$endgroup$
– TonyK
Jan 17 at 10:50
$begingroup$
It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
$endgroup$
– TonyK
Jan 17 at 10:50
add a comment |
1 Answer
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It is just a matter of aesthetics. Personally, I find it quite unaesthetic to see $a_1times a_2timesldotstimes a_n$, compared with $a_1times a_2timescdotstimes a_n$. But there is nothing wrong with it.
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
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add a comment |
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$begingroup$
It is just a matter of aesthetics. Personally, I find it quite unaesthetic to see $a_1times a_2timesldotstimes a_n$, compared with $a_1times a_2timescdotstimes a_n$. But there is nothing wrong with it.
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
$endgroup$
add a comment |
$begingroup$
It is just a matter of aesthetics. Personally, I find it quite unaesthetic to see $a_1times a_2timesldotstimes a_n$, compared with $a_1times a_2timescdotstimes a_n$. But there is nothing wrong with it.
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
$endgroup$
add a comment |
$begingroup$
It is just a matter of aesthetics. Personally, I find it quite unaesthetic to see $a_1times a_2timesldotstimes a_n$, compared with $a_1times a_2timescdotstimes a_n$. But there is nothing wrong with it.
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
$endgroup$
It is just a matter of aesthetics. Personally, I find it quite unaesthetic to see $a_1times a_2timesldotstimes a_n$, compared with $a_1times a_2timescdotstimes a_n$. But there is nothing wrong with it.
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
answered Jan 17 at 10:40
José Carlos SantosJosé Carlos Santos
160k22127232
160k22127232
add a comment |
add a comment |
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$begingroup$
$Acdot Bcdot ldots cdot K$ looks strange to me
$endgroup$
– Henry
Jan 17 at 10:43
$begingroup$
In ordinary text, an ellipsis is used to indicate omitted material which the writer might not expect the reader to guess from the context. In maths, sometimes the context makes it clear what the omitted material is, and sometimes it doesn't. Can we use the typographical difference to indicate the difference in meaning?
$endgroup$
– Rosie F
Jan 17 at 10:48
1
$begingroup$
It's just that $a,b,ldots,z$ and $a+b+cdots+z$ look nicer than $a,b,cdots,z$ and $a+b+ldots+z$. There's no difference in meaning.
$endgroup$
– TonyK
Jan 17 at 10:50