Re: Relative Cardinality
- From: David Kastrup <dak@xxxxxxx>
- Date: Sun, 03 Jul 2005 12:10:51 +0200
mueckenh@xxxxxxxxxxxxxxxxx writes:
> Relative Cardinality
>
> Given two finite or infinite sets A and B with elements a e A and b e
> B. The union of these sets does exist. If the elements can be put into
> an order < (not necessarily a well-order) such that in this order
> 1) there are all elements a e A and b e B
> 2) there are never two elements b,b' e B without an element a e A
> between them with respect to <
> then the cardinality Card(B) of B is not larger than the cardinality
> Card(A) of A:
> Card(B) =< Card(A).
So Card({1,3}) =< Card({2}).
And card({1}) =< Card({}).
Great. Do you even check your nonsense with trivial examples? Apart
from that, cardinality of a set is a property of the number of
elements, and not of their values. So orderedness is not fundamental
to cardinality. Bijections are.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.
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