Re: Cantor's definition of set

John Jones schrieb:
On Oct 29, 5:02?pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Oct 27, 2:52 am, John Jones <jonescard...@xxxxxxx> wrote:

But a sequence is a certain kind of set that "codes" the order.
There's no conflict in that.
In that case, the set should incorporate that code in the name of the
set.
So instead of saying 'a set of numbers', I should also include in
the name of the set the application for generating numbers. But in
that case, I simply have an application.
Another of your dicta.

A dog that quacks like a duck, looks like a duck, swims and flies like
a duck, is a duck. So why call a function for generating numbers a
set?

Functions can be viewed as sets with certain properties.
But not all sets do have these properties. So its handy
to call functions functions and not sets.

Your dog example is the analog of the implication from
function to set. But natural language, words, in their
semantic field, often also convey the other direction.
And the other direction is that there is no necessary an
implication from set to function, or if you want from
ducks to dogs. Not every duck is a dog.

This is basic use of language and should be even
clear to a philosopher. Exercise for you as a philosopher,
make a better analog than dog and duck for functions
and sets.

It's true that "x is a set iff x is a formula" is not the case. But,
in certain treatments, formulas are sets.

I have to ask you - what is 'in certain treatments'? Is there a
treatment that we can employ for transmuting one thing into another
thing? If you say yes, then
1) either sets and functions are already related, which begs the
question, OR
2) 'treatment' must refer to a transcendent metaphysical agent for
transmuting incommensurables, like sets and functions, one into the
other.


Treatment here referes to a certain set theories I assume.
You find a list of "treatments" here:
http://en.wikipedia.org/wiki/Set_theory

The metaphysical agents in a treatment are the axioms,
which can state relationships in the object level.

Sets and functions are not incommensurable. If a
function f is viewed as a set, which is often denoted
by graph(f) and the lingo is that this set is the
graph of the function, then we can related it very
easily to a set s.

And it might even be the case that the graph(f)
and the set s have the same cardinality. For example
if we have:

A={1,2}
B={3,4}

graph(f) = {<1,3>,<2,4>}, i.e. the
function that sends 1 to 3 and 2 to 4.
s={<1,3>,<1,4>}, i.e. the relation
that relates 1 to 3 and 4.

Here we have:
card(graph(f))=card(s)=2.

Welcome on planet math. Have you landed now?

Bye
.

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