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Richard Dore
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"A gentleman never chooses a basis."

Around these parts, the aphorism "A gentleman never chooses a basis," has become popular.

Is there a gentlemanly way to prove that the natural map from V to V** is surjective if V is finite dimensionsal?

As in life, the exact standards for gentlemanliness are a bit vague. Some arguments seem to be implicitly pick basis. I'm hoping there's an argument which is unambigously gentlemanly.

Richard Dore
  • 5.3k
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  • 36
  • 43