Re: Heap-Set Theory H-S

On Jan 29, 2:45 pm, G. Frege <nomail@invalid> wrote:
On Tue, 29 Jan 2008 14:29:16 -0800 (PST), Zaljo...@xxxxxxxxx wrote:

Also I was trying to find a symbol to represent heaps , something
that is comparative to the brackets { } of sets.

I once proposed [ ] for that.

        [x, y, z]

Then we have

        x c [x, y, z].

Where "c" denotes "is a constituent". (You'd say "part", I guess.)



You see there is no need for the coma between the members of a heap

Sometimes it may be helpful:

        1 c [1, 2, 3].



'x' =x
'y'= y

x is atomic part of 'xy'
x is atomic part of x
y is atomic part of 'xy'
y is atomic part of y
'xy' is a part of 'xy'

Right.

        x = [x],

        [x, y] c [x, y],

etc.

An interesting feature of heaps is that they are "flat" (i.e. there is
-in contrast to sets- no hierarchy if heaps), for example

        [[x, y], z] = [x, y, z].

F.

--

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

Exactly!

but Frege I also had [ ] in my mind , but I see it too heavy for that
purpose.

I wanted the lightest symbole,

Ideally we would use spaces to do the job

so for example we say z = xy

so xy here is actually the heap of xy

but I feel that a lot of objections will be raised against that

so I prefered to use the lightest symole like ' ' , so 'xy'
would be the nearest to xy, I guess?

I like your notation c to represent 'is a constituent of' or what I
call ' is part of' .


But what is interesting to me is that if we stipulate that all sets
are atomic ( NOTE: this is not the standard , that standard is to
stipulate that all singlton sets are atomic: Review David Lewis in
Parts of Classes ) However in this theory I stipulated that all sets
are atomic,
and from comprehension in this theory we can actually get the heap of
any sets that we fullfill P(x) for any P(x) provided that there should
exist at least one set for which P holds.

So in this way we can have the heap of all ordinals, the heap of all
sets, the heap of all well founded sets, the heap of all sets
bijective to a set, the heap of all sets bigger than a set, etc...,
the heap of all sets other than a set, the heap of all sets that are
not members of a set etc....

Zuhair

.

Relevant Pages

  • Re: Heap-Set Theory H-S
    ... But what is interesting to me is that if we stipulate that all sets ... this is not the standard, ... is not a "molecular" heap - but just a heap consisting of that very set. ... of course there's no "empty heap", ...
    (sci.logic)
  • Re: Storage of Variables
    ... The heap is specifically defined in the C language AFAICR. ... The heap is not in the index of the standard. ... The stack and the data segment are generally identical. ...
    (comp.os.linux.misc)
  • Re: Off Topic: Stack vs. Heap
    ... > Is the concept of stack and heap completely independent of the standard? ... The standard defines static, dynamic and automatic storage duration, ...
    (comp.lang.cpp)
  • Re: How to calculate the stack and heap size
    ... How can we calculate the stack and heap size requried by a C program. ... There is no standard way to determine how much heap us used because ... It depends on how good your implementation is at reusing freed memory ...
    (comp.lang.c)
  • Re: "Reverse" heapify
    ... the above discussion assumes that my beam is ... I'm building a heap bit by bit. ... >parent should be swapped. ... it should be the standard way of building a heap rather than the ...
    (comp.programming)
Loading