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SHOW that the rational numbers are listable, hence the set of them is countable.
A complex number that is the root of a polynomial with integer coefficients is called "algebraic."
SHOW that the set of algebraic numbers is countable.
SHOW that nonalgebraic numbers exist...not every complex number equals to root of a polynomial with
integer coefficients.
HOMEWORK: Suppose |S| = m and |T| = n. How many injective functions are there from S to T? Can you find a formula or
an algorithm for computing this...with justificiation?
How about surjective?
Bijective?
Find injections from P(N) to the reals, and from the reals to P(N).
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Hi it looks that it's discrete math issues. I am mathematician and can solve and explain you the solution. Is solution on papes enougn or you also need verbal explanation?