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Science Forum Index » Mathematics Forum » Names for Parts in Sigma-Notation
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| Marc van Dongen |
 Posted: Tue Apr 29, 2008 11:29 pm |
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Dear forum,
I have a few questions which are related to the Sigma notation for
summation.
My first question is as follows: given the expression $\sum^{n}_{i =
0} f( i )$, $f( i )$ is called the summand, and I've seen $i$ being
referred to as index variable. Is there a generally accepted name for
the expressions which define the lower and upper bounds for the index
variable? Stated differently, are there generally accepted names for
the expression $n$ and $i = 0$?
My second question is as follows. Is there a name for the equivalent
of summand in the product notation? So what is $f( i )$ called in $
\prod^{n}_{i = 0} f( i )$?
My next question is as follows. Is there a name for the equivalent of
summand in general expressions such as $\cup^{n}_{i = 0} f( i )$, $
\int^{n}_{i = 0} f( i )$, etc.
Finally, is there a generally accepted term for expressions of the
form $X^{n}_{i = 0} f( i )$, where $X$ is $\sum$, $\prod$, $\cup$, and
so on?
I am also interested in any references.
Thanks in advance for your help.
Regards,
Marc van Dongen |
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| Marc van Dongen |
| Posted: Wed Apr 30, 2008 12:19 am |
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On Apr 30, 10:50 am, William Elliot <ma...@hevanet.remove.com> wrote:
Quote: In, sum(i=n,m) f(n)
capital sigma is the sum sign, i the index, n the lower limit,
m the upper limit. Perfably the lower limit is first as sum_n^m.
Thanks.
Quote: My second question is as follows. Is there a name for the equivalent
of summand in the product notation? So what is $f( i )$ called in $
\prod^{n}_{i = 0} f( i )$?
Yes, capital Pi.
I'm aware of this, but I'd like to know the equivalent of sum*mand*.
Quote: If C is a connection of sets, then \/C is the great union of C.
If C = { Aj | j in I } is an index collection of sets, then
\/C = \/{ Aj | j in A } = \/_j Aj
If j is over integers from n to m, then you can write
\/_n^m Aj (yuck) or \/_(j=n,m) Aj (better).
Thank you, but what would you call the expression which is being
``accumulated'' in summation, multiplication, integration, union,
intersection, and so on.
To state this differently, let's define Accumulation( i, lo, hi, op )
f( i ) as neut( op ) op f( lo ) op .. op f( hi ), where neut( op ) is
the neutral element of the operation op. Then we can define
Sum(i=lo,hi) f( i ) = Accumulation( i, lo, hi, + ) f( i ),
Product(i=lo,hi) f( i ) = Accumulation( i, lo, hi, * ) f( i ), and so
on. Is there a name for f( i ) in Accumulation( i, lo, hi, op )
f( i )? (For Accumulation( i, lo, hi, + ) f( i ) you'd call it
summand, but I'm interested in a general name.)
Quote: Finally, is there a generally accepted term for expressions of the
form $X^{n}_{i = 0} f( i )$, where $X$ is $\sum$, $\prod$, $\cup$, and
so on?
Finite sums, products, unions, etc.
Don't forget infinite sums, products, unions.
Even uncountable sums (of disjoint spaces) and unions (of sets).
Thank you,but I'm interested if there is a name for the construct in
general, so a general name for an expression of the form Sum( i = 0,
n ) f( n ), Product( i = 0, n ) f( n ), Intersection( i = 0, n )
f( n ), and so on.
Regards,
Marc van Dongen |
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| Marc van Dongen |
| Posted: Wed Apr 30, 2008 9:06 pm |
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On Apr 30, 2:30 pm, "G. A. Edgar" <ed...@math.ohio-state.edu.invalid>
wrote:
Quote: In article
Thanks again, but it's not quite what I'm looking for. I'd like to
know if htere's a name which I can use for summand, multiplicand,
integrand, and similar terms which are used in similar kinds of
operations.
operand
Thanks.
Regards,
Marc van Dongen |
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