Re: infinity
- From: "zuhair" <zaljohar@xxxxxxxxx>
- Date: 27 Oct 2005 07:38:57 -0700
Matt wrote:
As Randy said, "arrangements" of a set do not have cardinality: they
have
ordinality. The set itself has one cardinality, independent of any
arrangements;
but the arrangements do not have cardinality.
----------------------------------------------------
The relation between cardinality and ordinality is a deep subject more
deeper than
you illustrated, in reality many times we cannot reach a specific
cardinality without ordinality
for example Aleph-1 is only reached through the Omegas with fields
having a cardinality of Aleph-0
So in reality it is the ordinal number Omega-1 is the one which gave
birth to Aleph-1 and not the reverse. I am doing something of that kind
in my question , but neither you nor Randy here figured what I am
trying to show. You will not solve matters by giving different
terminology for things , a thing which has ordinal number has
cardinality also.
But if you insist I will use your language , if set S can be equally
defined in a way that do not involve order and that can be rearranged
in the arrangment I pointed and can be bijected to Peano's set of
natural numbers starting from zero(which is impossible)
then and only then I will say the cardinality of set S is Aleph-0.
Cardinality is not that seperate from ordinality , they are different
of coarse but still one depends on the other , the generation of the
(Omega-x)s in Cantorian analysis and the Cardinals that comes from them
the (Aleph-[x+1})s is a good example of what I am saying
However I will wright a post on that matter to the group soon.
And generally speaking I think I figured out the difference in views
between TOmatics and mine and Ross on one side and the standard views
adopted by mathematicians on the other side, I think it is
philosophical and I will wrigth something on that soon.
Zuhair
.
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