Re: powerset with cardinality of 3^n

David R Tribble wrote:
>> This can be done if we treat the members of S as strings formed
>> from some alphabet of symbols. For simplicity, we'll use the
>> alphabet of decimal digits {0,1,2,...,9}, which limits our elements
>> to strings of digits, i.e., decimal integers.
>> ...

Ross A. Finlayson wrote:
> Maybe you are considering multivalent (multi-valued) logic.
>
> If you have a set, and it's the union of two sets of identical
> elements, for example Russell's socks, it contains only one element. A
> multiset can contain multiple copies of identical elements, and is
> different than a set, from pure set theory.

Something like that, yes. I was trying to come up with a way for each
element to have three (or more) values in any given subset, besides
the binary "present" and "not present". Multivalued logic would work,
which is essentially equivalent to what I've done using element
strings.

(I believe I've heard a multiset called a "bag" somewhere before,
but don't quote me on that.)

There's nothing earth-shattering here, just an interesting little
exercise in powersets and cardinalities.

It would get really interesting is if we could construct subsets
where we could derive an infinite number of values from each original
element. Then the cardinality of our resulting w-powerset would
probably be larger than the regular powerset.

.

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