LL-L "Lexicon" 2004.01.22 (04) [E]

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From: fvanlamoen at planet.nl <fvanlamoen at planet.nl>
Subject: LL-L "Lexicon" 2004.01.21 (12) [E]

Dear Sandy,

> From: Sandy Fleming [sandy at scotstext.org]
> Subject: "Lexicon"
>
> > From: Floor en Lyanne van Lamoen <fvanlamoen at planet.nl>
> > Subject: LL-L "Lexicon" 2004.01.21 (04) [E]
> >
> > I don't expect you to be a mathematician!! The thing is that
> > mathematicians
> > sometimes use language that differs from the everyday use. The
> > discussion of
> > historia matematica was funny, because it was agreed that
> "Anzahl" means
> > "cardinality", a concept of which I doubt that "normal people"
> > have any idea
>
> Speaking as a mathematician, but _not_ as a linguist (in fact
> I don't know much German) while "Anzhal" might be taken to mean
> "cardinality", this is not a good way, mathematically speaking,
> to distinguish it from "Zahl".
>
> > Die Anzahl der auf diese Weise gebildeten Zahlen ist unendlich.
> > The number (Anzahl) of numbers (Zahlen) formed in this way are
> infinite.
> In this sentence _all_ numbers mentioned, both the number of
> numbers involved and each number in the set, are cardinal numbers.

You are missing the point here. The word Anzahl is used when the number
describes a cardinality. So 2 as the amount of people in this room describes
a cardinality, but 2 as the result of the infinite sum of (1/2)^n does not,
despite the fact that 2 is a cardinal number. Zahl is for the more broad
concept of  "number".
I believe that Cantor's sentence is taken from his diagonal argument, so
that the Zahlen are rational numbers, i.e. generally no cardinal numbers.

The term cardinality was not brought up to distinguish from ordinal numbers,
but from the general concept of number.

> In English I would say "The number of numbers formed in
> this way is infinite", just as I'd say "The number of
> stars in the sky seems infinite", _not_ *"The number of
> stars in the sky seem infinite". The translation actually
> seems to contain an error which I find to be quite common
> amongst English-speaking technical writers, that of making
> a verb agree with the previous noun instead of the noun it
> applies to.

I am glad to read this. It is what I would have thought. I as thinking that
I would have made many mistakes in this.

The cofusion may have risen from:

"A lot of people are ... " where probably gramatically more correct would be
"a lot of people is ...".

Kind regards,
Floor.

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