Re: The Difference between a Set and an Element


JohnCreighton_@xxxxxxxxxxx wrote:
Frederick Williams wrote:
.... What is the physical difference between me and a
set containing me?

The difference is that you exist and the set containing
you does not. This allegation that sets can contain concrete
objects is misleading. Sets are abstract. Speaking as though
sets of concrete objects existed is just that, a way of speaking.
It's metaphorical. You shouldn't pretend that it really means that,
or if you do, you need to realize that you ARE pretending.


The set of bids is a lot more tangible then sets built up from the
power set of nothing.

Not really. "The set of bids" does not exist, and sets built up
from the empty set are, precisely as you point out, not tangible.
So neither of them is tangible at all, so it cannot be the case
that one of them is more tangible than the other, although the
bids are tangible.

ZPC gives us a directory structure with nothing
in it.

That is NOT true. A DIRECTORY *is* something, EVEN when there
are no files in it.

If I wanted to know if two computers contain the same files, I
would not check to see if the same files are stored in the same
directory.

The same files would HAVE to be stored in the same directories
if the computers were going to have the same files, because directories
themselves ARE ALSO files, and if one of them has a different
subdirectory
structure on one computer than on the other, or has differently-named
files in it, then THAT directory IS DIFFERENT between the two
computers,
and the file containing it IS DIFFERENT, so they DO NOT contain the
same files.

You're forgetting something about "file": "file", like "set", "string",
and
"category", provides a Comprehensive Netural Framework, also known,
when were talking math instead of media, as an Alternative Foundation.
My point is that ANY concept can be REPRESENTED AS a file, or a set,
or a bit-string, or, a category. And if that's how your hard-drive is
organized,
then EVERYthing on it is a file, until you get down to strings that
aren't.
And you would never NEED to have strings that aren't files, IF you
didn't
WANT to. Anything that you could represent via a non-file string, you
could
ALSO RE-represent AS A FILE whose NAME was the SAME string.

.

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