What is the equivalent of integration while multiplying continuous values? [duplicate] Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Can there be a symbol for continuous product?What is the difference between discrete and continuous mathematics?Can we possibly exchange summation and integration with negative values?continuous function and max/min valuesWhat happen to composite of infinite number of continuous functions?What is the counting sequence of a Binary String?Can I derive the formula for expected value of continuous random variables from the discrete case?What is the limit definition of the derivative equivalent for integration?Can a continuous function reach from a finite to infinite values on a closed interval?False statements about the continuous on the interval functionWhy does a differential factor appear when going from discrete summation to continuous summation?
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What is the equivalent of integration while multiplying continuous values? [duplicate]
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Can there be a symbol for continuous product?What is the difference between discrete and continuous mathematics?Can we possibly exchange summation and integration with negative values?continuous function and max/min valuesWhat happen to composite of infinite number of continuous functions?What is the counting sequence of a Binary String?Can I derive the formula for expected value of continuous random variables from the discrete case?What is the limit definition of the derivative equivalent for integration?Can a continuous function reach from a finite to infinite values on a closed interval?False statements about the continuous on the interval functionWhy does a differential factor appear when going from discrete summation to continuous summation?
$begingroup$
This question already has an answer here:
Can there be a symbol for continuous product?
1 answer
We know that summation is for discrete values, and integration is the generalization of summation so that it can be extended to continuous values.
We also have product for discrete value, what is its continuous counter part?
calculus discrete-mathematics
edited Mar 26 at 14:28
JJJ
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
$endgroup$
marked as duplicate by J. M. is a poor mathematician, Cesareo, clathratus, Theo Bendit, Eevee Trainer Mar 27 at 4:21
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
|
show 2 more comments
$begingroup$
This question already has an answer here:
Can there be a symbol for continuous product?
1 answer
We know that summation is for discrete values, and integration is the generalization of summation so that it can be extended to continuous values.
We also have product for discrete value, what is its continuous counter part?
calculus discrete-mathematics
edited Mar 26 at 14:28
JJJ
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
$endgroup$
marked as duplicate by J. M. is a poor mathematician, Cesareo, clathratus, Theo Bendit, Eevee Trainer Mar 27 at 4:21
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11
|
show 2 more comments
$begingroup$
This question already has an answer here:
Can there be a symbol for continuous product?
1 answer
We know that summation is for discrete values, and integration is the generalization of summation so that it can be extended to continuous values.
We also have product for discrete value, what is its continuous counter part?
calculus discrete-mathematics
edited Mar 26 at 14:28
JJJ
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
$endgroup$
This question already has an answer here:
Can there be a symbol for continuous product?
1 answer
We know that summation is for discrete values, and integration is the generalization of summation so that it can be extended to continuous values.
We also have product for discrete value, what is its continuous counter part?
This question already has an answer here:
Can there be a symbol for continuous product?
1 answer
calculus discrete-mathematics
calculus discrete-mathematics
edited Mar 26 at 14:28
JJJ
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
edited Mar 26 at 14:28
JJJ
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
edited Mar 26 at 14:28
JJJ
1317
edited Mar 26 at 14:28
JJJ
1317
edited Mar 26 at 14:28
JJJ
1317
1317
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
asked Mar 25 at 18:14
VARUN.N RAOVARUN.N RAO
124
124
marked as duplicate by J. M. is a poor mathematician, Cesareo, clathratus, Theo Bendit, Eevee Trainer Mar 27 at 4:21
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by J. M. is a poor mathematician, Cesareo, clathratus, Theo Bendit, Eevee Trainer Mar 27 at 4:21
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11
|
show 2 more comments
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Try: Integration of the logarithm.
Adding logarithms corresponds to multiplication.
Integration corresponds to summation.
So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.
But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Try: Integration of the logarithm.
Adding logarithms corresponds to multiplication.
Integration corresponds to summation.
So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.
But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
add a comment |
$begingroup$
Try: Integration of the logarithm.
Adding logarithms corresponds to multiplication.
Integration corresponds to summation.
So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.
But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
add a comment |
$begingroup$
Try: Integration of the logarithm.
Adding logarithms corresponds to multiplication.
Integration corresponds to summation.
So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.
But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
Try: Integration of the logarithm.
Adding logarithms corresponds to multiplication.
Integration corresponds to summation.
So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.
But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
edited Mar 27 at 6:05
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
answered Mar 25 at 20:51
David G. StorkDavid G. Stork
12.2k41836
12.2k41836
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
add a comment |
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course).
$endgroup$
– YiFan
Mar 26 at 6:06
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
$begingroup$
David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral
$endgroup$
– Eevee Trainer
Mar 27 at 4:20
1
1
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
@EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer.
$endgroup$
– YiFan
Mar 27 at 5:46
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
$begingroup$
Oops, my bad lol.
$endgroup$
– Eevee Trainer
Mar 27 at 5:57
add a comment |
$begingroup$
There is none. How would one define it in a consistent manner?
$endgroup$
– Don Thousand
Mar 25 at 18:18
$begingroup$
I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it
$endgroup$
– VARUN.N RAO
Mar 25 at 18:27
$begingroup$
Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration.
$endgroup$
– Don Thousand
Mar 25 at 18:29
$begingroup$
Integration of the log?
$endgroup$
– David G. Stork
Mar 25 at 19:18
$begingroup$
That seems to be wonderful!!
$endgroup$
– VARUN.N RAO
Mar 25 at 20:11