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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| An observaton on suggestion 2:
The problem with changing the formal definition would be that f:X\to{1,2,3,...} is not the same thing as f being a cardinal-valued mapping. A mapping to the cardinal numbers (or even to the nonzero cardinals) is more general in that it allows for "infinite" multiplicities (\aleph_0, \aleph_1, etc.) that are not permitted in the mapping to the positive integers.
A question regarding suggestion 4:
I'm a bit confused by this, since I don't think every multiset can actually be represented as a *sequence* of (element, multiplicity) pairs. For example, if M = (R+, f) where R+ are the positive real numbers and f(x) = ceil(x), this should be a valid multiset, but cannot be represented as a sequence. As far as I am aware, either of these representations only works for finite multisets. Am I missing something? |
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