# Which are Bases?

Algebra Level 3

Which of the following are "bases" in the way described?

1. $$(2,\,3)$$ and $$(-1,\,1)$$ generate $$\mathbb{R}^2$$ over the real numbers.
2. $$\dots,\,2^{-2},\,2^{-1},\,2^0,\,2^1,\,2^2,\,\dots$$ generate real numbers by using their binary representation over $$\mathbb{F}_2$$.
3. $$1$$ and $$\sqrt{2}$$ generate the algebraic numbers over the rationals.
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