# Re: integrals

• To: math-font-discuss@cogs.susx.ac.uk
• Subject: Re: integrals
• From: jeremy@cs.aukuni.ac.nz (Jeremy Gibbons)
• Date: 07 Aug 1993 16:50:36 +1200

> >Can somebody tell me why there is a small integral in cmex, and in cmsy.
> >\int refers to the one in cmex.
>
> It's used in areas of mathematics where integration is seen as a
> function from a set to a number, so:
> $> \smallint\{e_i \mid i \in I} >$
> rather than:
> $> \int_{i \in I} e_i >$
> Similarly, some mathematicians use \Sigma and \Pi rather than \sum and
> \prod.  (Jeremy, have you got references for this usage, this is your
> sort of field?)

I'm not sure I understand. \sum and \prod produce a big sigma and pi,
respectively, don't they? Are you referring to the "Eindhoven Quantifer
Notation", which uses

$(\Sigma i \mathbin{:} 0 \le i < n \mathbin{:} i^2)$

for the sum of the squares of the first $n$ naturals? If so, you could see
Dijkstra & Feijen, "A Method of Programming" (Addison-Wesley, 1988), but
they actually use an uppercase "S" instead of a Sigma because it is
"typewritten". (Looks awful, too.) Anne Kaldewaij's "Programming: The
Derivation of Algorithms: (Prentice Hall, 1990) does use a Sigma, though.

Doesn't apply to integrals, though. (Can you integrate over countable sets?
I've only ever seen it done over reals or complex nos...)

Jeremy