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Homework Statement
Find the cardinality of the set of all equivalence relations on N
Homework Equations
by what we have learned yet we only have to determine if it's countable or not
The Attempt at a Solution
I know that the set of all relations on N is equivalent to P(NXN) thus is not countable, so the set of all equivalence relation is a subset of P(NXN) though it doesn't help me much.
I also know that each equivalence relation devides N to a countable number of equivalence classes, but each equivalence relation is just one object of "the set of all equivalence relations" so I don't know what to do with it either.
Homework Statement
find the cardinality of the set of all injective functions from N to N
Homework Equations
The Attempt at a Solution
same as before, I really don't know where to begin