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The author here appears to be working with what I would call "multi-sets" in which a particular element can appear more than once. So the multi-set {1,1} for instance has two elements. But it has only one "distinct element".Summary:: Kinda confused.
It says that sets that are equal ie having the same types of elements can also be equivalent, having the same number of elements when b has more distinct elements than a. Please explain
In the text you quoted, the notation "##B = \{d,d,c,c,b,b,a,a\}##" is intended to denote a set with 4 distinct elements, For example, the notation "##d,d##" does not denote two distinct things both denoted by a "##d##". Instead it denotes the same thing ##d## listed twice. This notation convention is followed when writing elements of sets.when b has more distinct elements than a. Please explain
My guess is that the author is setting you up to consider sets that are not equal, but are equivalent, such as with certain infinite sets. For example, the set of natural numbers {1, 2, 3, ...} is equivalent to the set of positive even integers {2, 4, 6, ...}. This seems counterintuitive at first, since the first set has apparently more elements in it, but as long as a one-to-one mapping can be found from each set to the other, both sets have the same cardinality.It says that sets that are equal ie having the same types of elements can also be equivalent, having the same number of elements when b has more distinct elements than a. Please explain