I'm sure there is a name for this paradox, but I haven't studied set theory enough to know what it's called. Can someone please help resolve this?
Let N = the set of the natural numbers, and let D = the set of natural odd numbers.
N and D have equal cardinalities, and yet N is unequal to D. This is not a problem, for two sets can have similar cardinalities while maintaining their uniqueness.
The problem, for me anyway, is this: N and D are both infinite sets, and N is a proper superset of D. Thus, shouldn't the cardinality of N be greater than that of D?
Shouldn't a set always have a cardinality greater than that of its proper subset?