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How can it happen to find infinite bases in $\mathbb R^n$ if $\mathbb R^n$ does not admit more than $n$ linearly independent vectors?

Also considered that each basis of $\mathbb R^n$ has the same number $n$ of vectors.

  • 0
    Why do you think it can for $n$ finite?2012-11-30
  • 0
    Do you mean that the set of bases of $\mathbb{R}^n$ is infinite?2012-11-30
  • 1
    It cannot happen.2012-11-30
  • 1
    I don't understand what you mean by "infinite bases."2012-11-30
  • 1
    Infinite basis over $\mathbb R$ or over $\mathbb Q$ ? ;)2012-11-30

5 Answers 5