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A Real Vector Space over the Rational Field is Infinite-Dimensional

Last updated Nov 1, 2022

# Statement

TODO

TODO

...

11/7/2022

- Rn\mathbb{R}^{n} over Q\mathbb{Q} is an Infinite-Dimensional Vector Space

Infinite-Dimensional Vector Space

Definition Let VV be a . We say that VV is an if it is not a . Remarks Note that this...

11/7/2022

(this uses countability of Linear Combination

Linear Combination

Definition Let VV be a on FF and let x1,…xn∈V\mathbf{x}{1}, \dots \mathbf{x}{n} \in V for some $n \in \mathbb{Z}{\geq...

11/7/2022

s with Rational Numbers as coefficients).

# Encounter

  1. Hoffman and Kunze - Linear Algebra - Section 2.3 Problem 14 pg 49

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A Real Vector Space over the Rational Field is Infinite-DimensionalTODOInfinite-Dimensional Vector Space/CountableLinear Combination/Rational NumbersReal Numbers/Hoffman and-Kunze-Linear-Algebra