Sorry Mike, (couldn't resist)
How flexible do you want the wrong answer?
From number theory, cardinal numbers start at 1.
That's why you can't use 0 as the lower bound of a cardinality. Therefore, UML uses the term multiplicity - which they have defined as 0..oo
The quote you have, from the Glossary, for cardinality is correct, but not of much direct use.
The UML definition (§7.3.32) for MultiplicityElement is: A multiplicity is a definition of an inclusive interval of non-negative integers beginning with a lower bound and ending with a (possibly infinite) upper bound. A multiplicity element embeds this information to specify the allowable cardinalities for an instantiation of this element.
Since, by defintion, when you instantiate an element you must have at least one instance, the definition holds good in both parts.
However, when dealing with the number of elements you might find at the end of a relation, which may be optional, the minimum number may be 0, therefore only the first part of the definition is really applicable.
For those of us who "grew up" in the data management world, the separation of cardinality and optionality is well understood - hence the "crows foot" symbology of the ER diagram. Multiplicity combines both into one concept.
What I am explicitly saying is:
1) You shouldn't need two concepts, one includes the other
2) if you do decide to have 2 concepts you actually need three (multiplicity, optionality, cardinality) and you must constrain all three according to the appropriate rules (not elaborated here).
Paolo
