Question

Prove for each of the following: a. Exercise A union of finitely many or countably many...

Prove for each of the following:

a. Exercise A union of finitely many or countably many countable sets is countable. (Hint: Similar)

b. Theorem: (Cantor 1874, 1891) R is uncountable.

c. Theorem: We write |R| = c the “continuum”. Then c = |P(N)| = 2א0

d. Prove the set I of irrational number is uncountable. (Hint: Contradiction.)

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