Re: The simplest way to understand sets.

[debaser]

musatov wrote to John Jones, et. al.:
On Nov 22, 6:49 pm, Jan Burse <janbu...@fastmail.fm> wrote:
> John Jones:
>
> >> He can't, because "inside" and "outside" are relationships to something
> >> that is only itself.
>
> Depends how you define "can".
'May' is the term I strongly prefer. Even in the non-positive case
'may not' is more precise.

Usually when a term is defined 'may' is more precise:
> in other terms predating the term itself, this can count as
> dropping. Because the term is only a shorthand for the
> predating term.
>
> So when I do a definition:
>
>         x = y :<=> Az(z in x <-> z in y)        (Def)
>
> Then "in" predates "=". And "=" is just a short hand for some
> formula using "in". Which means that we can drop "=", everything
> that is said by using "=", can also be said by using "in".
>
> This is the nature of non recursive definitions. They can
> be expanded and are only here for convenience.
>
> I would say its possible to drop equality from set theory,
> we can formulate everything alone by the use of membership.
> Lets make a test. Zuhair defined:
>
>         y inside x :<=> x in y
>         y outside x :<=> not y in x and not x=y.
>
> When we use the above cast of set theory where "=" is a
> definition, then the second definition is equal to
> saying:
>
>          y outside x :<=> not y in x and exists z(z in x xor z in y)
>
> Nice, isn't it.
>
> Bye
-------------------------------------------

please notice illustrations:

*example 1*

-----------
Equation 1
-----------
x
i * --- = a
y

-----------
Equation 2
-----------
y
i * --- = b
x

-----------
Equation 3
-----------

i
y * --- = c
x

-----------
Equation 4
-----------

x
y * --- = d
i

-----------
Equation 5
-----------

i
x * --- = e
y

-----------
Equation 6
-----------

y
x * --- = f
i

let (a + c + e) = n

let (b + d + f) = p

(a + c + e) - (b + d + f) = n - p

(a + c + e) + (b + d + f) = n + p

-----------------------------------------------
in coding, perhaps as you referenced inside-out
-----------------------------------------------

<mode></code> \
\
=inside
/
</mode><code> /

<code></mode> \
\
= outside
/
/
</code><mode>

-----------------------------

<mode></code> \ / <code></mode>
\ /
outside=in
/ \
</mode><code> / \ </code><mode>

-----------------------------

</code><mode> \ / </mode><code>
\ /
inside=out
/ \
<code></mode> / \ <mode></code>

--------------------------------

Musatov