Re: Names for Parts in Sigma-Notation

On Apr 30, 10:50 am, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:

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.

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*.

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.)

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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