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  3. 1)show that a subset of a countable set is also co

1)Show that a subset of a countable set is also countable. 2) Let P(n) be the...

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Advance Math

1)Show that a subset of a countable set is also countable.
2) Let P(n) be the statement that 13 + 23 +· · ·+n3 =(n(n +1)/2)2 for the positive integer n.
a) What is the statement P(1)?
b) Show that P(1) is true, completing the basis step of
the proof.
c) What is the inductive hypothesis?
d) What do you need to prove in the inductive step?
e) Complete the inductive step, identifying where you
use the inductive hypothesis.
f ) Explain why these steps show that this formula istrue
whenever n is a positive integer.

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