Solution Found!
Let V be the set of real numbers regarded as a vector space over the field of rational
Chapter 1, Problem 3(choose chapter or problem)
QUESTION:
Let V be the set of real numbers regarded as a vector space over the field of rational numbers. Prove that V is infinite-dimensional. Hint: 62 Chap. 1 Vector Spaces Use the fact that IT is transcendental, that is, it is not a zero of any polynomial with rational coefficients.
Questions & Answers
QUESTION:
Let V be the set of real numbers regarded as a vector space over the field of rational numbers. Prove that V is infinite-dimensional. Hint: 62 Chap. 1 Vector Spaces Use the fact that IT is transcendental, that is, it is not a zero of any polynomial with rational coefficients.
ANSWER:Step 1 of 2
We have
Take then
is neither represented as
Where and nor represented as a linear combination of rational.