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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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