Sigma notation for iterating through number of members of a set with constant expression
$begingroup$
Say I have a graph G and I want to sum some constant C (like the minimum degree of the graph) for every vertex. Can I use the following notation?
$$sum_{x in V(G)}C $$
Is this an appropriate way to use sigma notation?
There is a similar question here Notation of the summation of a set of numbers
but it doesn't account for the fact that the expression could be a constant. A person I am working with questioned it and I couldn't find any resources where it is used in this manner. I don't see why it would be improper because you could have an expression like $sum_{i=1}^{n}C$.
Thank you
graph-theory summation proof-writing notation
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
$endgroup$
add a comment |
$begingroup$
Say I have a graph G and I want to sum some constant C (like the minimum degree of the graph) for every vertex. Can I use the following notation?
$$sum_{x in V(G)}C $$
Is this an appropriate way to use sigma notation?
There is a similar question here Notation of the summation of a set of numbers
but it doesn't account for the fact that the expression could be a constant. A person I am working with questioned it and I couldn't find any resources where it is used in this manner. I don't see why it would be improper because you could have an expression like $sum_{i=1}^{n}C$.
Thank you
graph-theory summation proof-writing notation
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
$endgroup$
$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16
add a comment |
$begingroup$
Say I have a graph G and I want to sum some constant C (like the minimum degree of the graph) for every vertex. Can I use the following notation?
$$sum_{x in V(G)}C $$
Is this an appropriate way to use sigma notation?
There is a similar question here Notation of the summation of a set of numbers
but it doesn't account for the fact that the expression could be a constant. A person I am working with questioned it and I couldn't find any resources where it is used in this manner. I don't see why it would be improper because you could have an expression like $sum_{i=1}^{n}C$.
Thank you
graph-theory summation proof-writing notation
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
$endgroup$
Say I have a graph G and I want to sum some constant C (like the minimum degree of the graph) for every vertex. Can I use the following notation?
$$sum_{x in V(G)}C $$
Is this an appropriate way to use sigma notation?
There is a similar question here Notation of the summation of a set of numbers
but it doesn't account for the fact that the expression could be a constant. A person I am working with questioned it and I couldn't find any resources where it is used in this manner. I don't see why it would be improper because you could have an expression like $sum_{i=1}^{n}C$.
Thank you
graph-theory summation proof-writing notation
graph-theory summation proof-writing notation
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
edited Dec 6 '18 at 22:09
Asaf Karagila♦
304k32430763
304k32430763
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
asked Dec 6 '18 at 21:59
rachelhowardrachelhoward
748
748
$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16
add a comment |
$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16
$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16
add a comment |
1 Answer
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$begingroup$
Indeed, you are correct, you can use $sum_{x in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to
$$
sum_{x in S} C = C cdot |S|,
$$
for any finite set $S$.
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
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add a comment |
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1 Answer
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active
oldest
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1 Answer
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active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Indeed, you are correct, you can use $sum_{x in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to
$$
sum_{x in S} C = C cdot |S|,
$$
for any finite set $S$.
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
$endgroup$
add a comment |
$begingroup$
Indeed, you are correct, you can use $sum_{x in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to
$$
sum_{x in S} C = C cdot |S|,
$$
for any finite set $S$.
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
$endgroup$
add a comment |
$begingroup$
Indeed, you are correct, you can use $sum_{x in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to
$$
sum_{x in S} C = C cdot |S|,
$$
for any finite set $S$.
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
$endgroup$
Indeed, you are correct, you can use $sum_{x in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to
$$
sum_{x in S} C = C cdot |S|,
$$
for any finite set $S$.
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
answered Dec 6 '18 at 22:06
gt6989bgt6989b
34k22455
34k22455
add a comment |
add a comment |
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$begingroup$
It looks logically correct, but why wouldn't you just write $lvert V(G)rvert cdot C$?
$endgroup$
– David K
Dec 6 '18 at 22:03
$begingroup$
We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted.
$endgroup$
– rachelhoward
Dec 6 '18 at 22:09
$begingroup$
OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly.
$endgroup$
– David K
Dec 6 '18 at 22:16