Re: set theory : the blunder

On Sat, 14 Jul 2007 14:07:53 EDT, tommy1729 <tommy1729@xxxxxxxxx>
wrote:

I said:


Your claim

(y,z) is y,z

is meaningless (at least in standard math lingo).

no its not.

Yes, it is.


[Consider:]

(x-3)(x-2) = 0

solution (3,2) or 3,2

This are two ways of giving the two solutions of the equation. Either
you use the "pair notation" (actually denoting a pair of numbers, i.e.
a certain _set_), or you just use a list of numbers, listing the two
solutions of the equation, here and 3 and 2.

This does not mean that the following identity claim (i.e. the
following expression) is "meaningful":

(3,2) = 3,2.

"(3,2)" denotes a certain pair (a set), the first element of which is
3 and the second element of which is 2. While on the other hand "3,2"
doesn't (in NO common set theory) denote a pair (or a set).


Try to FORMALIZE it in a logical system of your
choice:

(x,y) = x,y [???]

it follows naturally from (x) = x

Huh? Well imho it "follows" naturally from the fact that you are a
crank.


Though

[[x,y]] = [x,y]

does make sense (in a certain framework),

and in a similar way (x,y) = x,y !

No. (Well, only if your framework is not a "standard" system, i.e. not
a standard system of mathematical logic.)


[x,y] = x,y

doesn't. (See comments above.)


To get some ground under our feet...:


For example, in my theory of heaps

"[y,x]"

is a name/term referring to a heap.

your theory ???

Right.


that means you disagree too on cantor :p

No, that means that I just considered an alternative framework (i.e. a
part/whole theory instead of a set theory).

I already told you that there are alternative theories out there. (Not
meant to REPLACE set theory of course.)


i haven't seen your theory...

So you missed my posts here. Well... :-/


you accused me before of not fully defining my replacement theory ,
but i haven't seen your theory which you suddenly dare to introduce)
either.

I recently posted 2 or 3 short accounts. In the present thread, or one
of it's relatives.


and if your theory has heaps in the way i have bags its stolen,

Well, heaps certainly do NOT behave like bags. That's for sure.


and you actually agree with me, and against cantor.

That's why I mentioned my theory in the first place.

Note that

"x,y"

is just a list of names/terms/variables (each of
which is referring to a heap - or whatever); but
"x,y" itself does not refer to a certain heap -
or whatever.

If you want to refer to the heap which has (at least)
x and y as constituents [you might] use the term

"[x,y]".


you assume x and y to be unique, this is not necessary.

Huh? I did what?


Here we have:

x c [x,y]
y c [x,y]

With other words, x and y are constituents of [x,y].


Now if we have x = [a, b], then

[x, y] = [[a, b], y] = [a, b, y].


F.


--

E-mail: info<at>simple-line<dot>de
.

Relevant Pages

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