Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

A number r ∈ R  is called algebraic provided for some n ∈ N there exists numbers  a0, a1, … , an ∈ Z such that r satisfies

p( r ) = 0

where p ( x ) = a0 + a1x + a2x2 + ⋯ + anxn.  

A number r ∈ R is called transcendental provided it is NOT algebraic

prove the set of ALL algebraic numbers is countable and the set of ALL transcendental numbers is uncountable.

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