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Guest
Posted: Fri May 02, 2008 12:31 pm
Hi all,

Definition:
R is z-total on x <-> AmexAnex(~m=n -> (mRn or nRm))

Definition:
y is R_bi-ended <-> EmeyEney(~Ec(cey cRm) ~Ec(cey nRc)).

Definition:
x is z-finite <-> ERAy(y is a non-empty subset of x ->
(y is R_bi-ended & R is z-total on y))

The standard definition of finite is:

x is finite <-> En(n is a natural number & n equinumerous to x)

Now the question is: is the following true in Z ?

x is z-finite <-> x is finite.

Zuhair
MoeBlee
Posted: Fri May 02, 2008 1:51 pm
Guest
On May 2, 3:31 pm, Zaljo...@gmail.com wrote:

Quote:
Definition:
R is z-total on x <-> AmexAnex(~m=n -> (mRn or nRm))

Definition:
y is R_bi-ended <-> EmeyEney(~Ec(cey cRm) ~Ec(cey nRc)).

Definition:
x is z-finite <-> ERAy(y is a non-empty subset of x -
(y is R_bi-ended & R is z-total on y))

The standard definition of finite is:

x is finite <-> En(n is a natural number & n equinumerous to x)

Now the question is: is the following true in Z ?

x is z-finite <-> x is finite.

Obviously, one direction is obvious.

MoeBlee
Guest
Posted: Fri May 02, 2008 3:16 pm
On May 2, 4:51 pm, MoeBlee <jazzm...@hotmail.com> wrote:
Quote:
On May 2, 3:31 pm, Zaljo...@gmail.com wrote:





Definition:
R is z-total on x <-> AmexAnex(~m=n -> (mRn or nRm))

Definition:
y is R_bi-ended <-> EmeyEney(~Ec(cey cRm) ~Ec(cey nRc)).

Definition:
x is z-finite <-> ERAy(y is a non-empty subset of x -
(y is R_bi-ended & R is z-total on y))

The standard definition of finite is:

x is finite <-> En(n is a natural number & n equinumerous to x)

Now the question is: is the following true in Z ?

x is z-finite <-> x is finite.

Obviously, one direction is obvious.

x is finite -> x is z-finite.

but how to prove

x is z-finite -> x is finite
Quote:

MoeBlee- Hide quoted text -

- Show quoted text -
 
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