- #1

- 66

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## Homework Statement

I know how to approach this problem; however, I'm just confused as to why we consider that R^2 is a vector space over the field R, and not Q or any other field for this question?

Standard basis vectors: e_1, e_2 or

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- Thread starter Mathematicsresear
- Start date

- #1

- 66

- 0

I know how to approach this problem; however, I'm just confused as to why we consider that R^2 is a vector space over the field R, and not Q or any other field for this question?

Standard basis vectors: e_1, e_2 or

- #2

member 587159

## Homework Statement

I know how to approach this problem; however, I'm just confused as to why we consider that R^2 is a vector space over the field R, and not Q or any other field for this question?

Standard basis vectors: e_1, e_2 ori,j

You will have difficulty writing down a basis of ##\mathbb{R}^2## over the field ##\mathbb{Q}##: such a basis is uncountably infinite and you need the axiom of choice to show it exists.

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