Which are Bases?

Algebra Level 2

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

  1. (2,3)(2,\,3) and (1,1)(-1,\,1) generate R2\mathbb{R}^2 over the real numbers.
  2. ,22,21,20,21,22,\dots,\,2^{-2},\,2^{-1},\,2^0,\,2^1,\,2^2,\,\dots generate real numbers by using their binary representation over F2\mathbb{F}_2.
  3. 11 and 2\sqrt{2} generate the algebraic numbers over the rationals.

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