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real question 1.doc
is also countable
Solution involves the proof of union of countable set is countable.
Real Analysis - 1- if A1,A2,A3,...,Am are each countable sets, then the union A1 U A2 U A3...U Am is countable
2- if An is a countable set for each n belong to N,then Un=1(to infinity) An is countable
Functions and countable sets - (See attached file for full problem description with all symbols)
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2.14 (I) Prove that an infinite set X is countable if and only if there is a sequence
of all the elements of X which has ...
Real Analysis - Sets & Proofs - A. If X and Y are countable sets, prove that their cartesian product X×Y is countable.
B. If X1, X2, X3, ... is a countable collection of countable sets, prove that their union is countable.
C. Th ...
Proof Set is Countable : Bolzano-Weierstrass Theorem - Given S is a subset of R
Suppose S' (set of all accumulation points in S) = emptyset
Prove S is countable.
I think I am supposed to use the Bolzano-Weierstrass Theorem but I can't figure out how ...