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- Is there a sense in which one infinite countable set can be bigger than another?
The uncountable sets [0,1] and [0,2] have the same cardinality ##2^{\aleph_0}##. Yet the second set is twice as big as the first set, in the sense of measure theory.
Is there something similar for countable sets, by which we can say that the set of integers is twice as big as the set of odd integers, despite the fact that they have the same cardinality ##\aleph_0##?
Is there something similar for countable sets, by which we can say that the set of integers is twice as big as the set of odd integers, despite the fact that they have the same cardinality ##\aleph_0##?