Re: Specifying Sets

On Mon, 10 Nov 2008 20:12:08 +0000, John Jones <jonescardiff@xxxxxxx> said:
...
In math, a sequence and a list denote (almost*) the same object,

Well quite obviously they don't, unless you want to say that mathematics
has no notion for one of them. If I ask you to bring a list of everyone
you knew, then I wouldn't expect it to be rule-sequenced. Yes? Yes.

He's talking about how "list" is used in mathematics, not in ordinary
English. And what he says is quite correct. A list in mathematics and
computer science (with some caveats in the latter case) is an ordered
sequence of objects. I do realize that just making stuff up about
mathematics based upon your naive and unschooled intuitions is your
modus operandi, and that this prevents you from actually doing the bit
of required research, but this is is just an empirically verifiable fact
about the usage of the term in mathematical contexts.

...
Which different words am I using? The set of all x reduces to all x.

So how would you reduce "The set of all solar planets has nine members"
to a statment about "all solar planets"?

'all x' is coherent. 'The set of all x' is not.

There is nothing extravagant is saying "the set of all blondes", above
all if you are doing mathematics.

But as you yourself indicate, there's no difference apart from
convention in saying 'the set of all x' and 'all x'. The former, is
therefore extravagent.

The point you seem to be missing is that sets are mathematical objects.
Reference to them therefore requires locutions like the former. "all x"
does not pick out a set, it simply quantifies over the x's and hence
will not do the job.

.

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