f a is not algebraic, then it is called transcendental. Let A denote the set of algebraic numbers and T be he set of transcendental numbers. 1. Show that A is countable. 2. Show that T is uncountable.

f a is not algebraic, then it is called transcendental. Let A denote the set of algebraic numbers and T be he set of transcendental numbers. 1. Show that A is countable. 2. Show that T is uncountable.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra

Problem 4E

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Question

A real number a is called algebraic if a is a root of a polynomial with integer coefficients.
If a is not algebraic, then it is called transcendental. Let A denote the set of algebraic numbers and T be
the set of transcendental numbers.
1. Show that A is countable.
2. Show that T is uncountable.

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