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# Re: integrals

• To: math-font-discuss@cogs.susx.ac.uk
• Subject: Re: integrals
• From: alanje@cogs.susx.ac.uk (Alan Jeffrey)
• Date: Sun, 8 Aug 93 16:09 BST


>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

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

That's precisely what I was referring to.

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

There's nothing stopping you integrating over a very countable set
like:
$\int_0^0 x dx$
:-)  Yes, normally integration is only performed over uncountable
sets, usually real invervals.  But there's no reason not to use
Eindhoven notation for uncountable sets, just because they have
a terminal case of construcivism doesn't mean everyone who uses
similar notation has to :-)

The \smallint is also used in the Duration Calculus of Hoare et. al:

CHP91
@Unpublished{CHP91:CalculusDurations,
author =      "Zhou Chaochen and C. A. R. Hoare and Anders P. Ravn",
title =       "A Calculus of Durations",
note =        "Oxford University Computing Laboratory",
}

This has probably appeared somewhere, sorry I don't have a fuller
reference.

Alan.