Re: Meaning of symbol in set theory?

"John H. Lindsay" <>
8 Dec 2000 22:24:00 -0500

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Meaning of symbol in set theory? (2000-12-06)
Re: Meaning of symbol in set theory? (Carl Offner) (2000-12-07)
Re: Meaning of symbol in set theory? (Sönke Kannapinn) (2000-12-08)
Re: Meaning of symbol in set theory? (John H. Lindsay) (2000-12-08)
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From: "John H. Lindsay" <>
Newsgroups: comp.compilers
Date: 8 Dec 2000 22:24:00 -0500
Organization: Posted via Supernews,
References: 00-12-018
Keywords: theory
Posted-Date: 08 Dec 2000 22:24:00 EST

M Sweger wrote:
> My question is what is the meaning of the symbol of the backwards
> capital E that is sometimes in bold. .....

The 'backwards capital E' means (a) there is a ...., or (b) there
exists at least one .... . Note also the upside down capital A,
which means for all .... (although some writers express this with
just a pair of parentheses, e.g. (x)(P(x)) which is then read, for
all x for which P(x) is true).

> Also in the above mentioned paper it talks about "Biconnectivity",
> "Strong Connectivity" and "Triconectivity" along with "fronds" and
> "cross-links". Have these concept ever been applied to Compilers and
> such? My compiler books mention DFS but don't address the
> connectivity issues.

Better dig back through the referenced previous works here; these
graph-theory terms get some strange takes applied to them by particular
writers or writers working in a particular areas.

> While I'm asking, do any papers for compilers try to apply Group
> Theory besides just Graph and Set Theory? .....

Dunno, never saw any.

> ..... The only paper I came
> across by Tarjan mentioned semigroups. I'll have to dig out a book on
> this to find the meaning of this term or go to the mathematical web
> page on its definition.

Semigroup: A set with one associative composition. The
existence of an identity element and invertability are not
assumed; if they were you'd have a group. There are
abelian or commutative semigroups. It's a big subject, and
harder to strangle theorems out of simce less is assumed.
It's useful in handling mathematical operators among many
other things. Only about half of the undergraduate Algebra
texts seem to deal with semigroups at all.

John H. Lindsay
48 Fairway Hill Crescent, Kingston, Ontario, Canada, K7M 2B4.
Phone: (613) 546-6988 Fax: (613) 542-6987

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