Re: A new definition for Cardinality

In article <1156349750.340494.28400@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"zuhair" <zaljohar@xxxxxxxxx> wrote:

Daryl McCullough wrote:
zuhair says...

I love this kind of discussion , but still I don't see how can this be
a proove , since it seem to work bothways to me.

since (x,y) is an element of f is always a false statement when f is
an empty set

then I can conclud the following

for all x, for all y : ( x,y) is an element of f implies that x is not
an element of A and y is not an element of B.

If you are starting with A = {} you are quite correct.
But that does not affect what goes on in the much more usual cases in
which A != {}.

Functions of form f:{} -> B are anomolous.

because you said "whatever V is so it is obvious that I can choose V as
" x is not an element of A and y is not an element of B "

This would also be true.

Not only that I can go even more than that

(x,y) is an element of f when f={ } implies that f is not an
injecitve function

A false statement implies any statement,

And at the same time I can state the following

(x,y) is an element of f when f={ } implies that f is an injective
funciton

According to your analysis then the relation { } which exists between A
and B when at least one of them is an empty set , this relation would
be both injective and not injective at the same time,

That depends.

If A != {} and B = {} then AxB = {} but there do not exist any functions
from A to B, since existence of a function from A to B requires that if
a in A then there exists some f(a) in B.

One must be very literal minded when dealing with definitions. It is a
talent that for most of us must be practiced for quite some time in
order to become good at it.

But it is a talent whose observance often irritates those who do not
have it excessively.


and this is
contradictive , and even if it is right then it proves that Cantor's
system will not work, This logic only proves that my system of ranking
cardinality is better than Cantor's since it is the one which can work
bothways weather { } is injective or not. Suprizingly you only proved
the superimacy of my system.

Zuhair

So you see your logic works both ways
.