is an infinite sequence of countable set. Recall that
for some positive integer i.}.
Prove that is countable. (In other words, prove that a countably infinite union of countable set is countable.)
is countable, where is an infinite sequence of countable sets.
is an infinite sequence of countable sets.
A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.
A function is onto function if each element in co-domain is mapped with atleast one element in domain.
Countable function should be one-to-one and onto.
Consider is an infinite sequence of countable sets such that
And so on.
The object is to prove is countable.
Now, let us take the union of all the elements of
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