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 a finite dimensional vector spacedimensionsal?
As in life, without choosing the exact standards for gentlemanliness are a basis?bit vague. Some arguments seem to be implicitly pick basesbasis. I'm hoping there's an argument which is unambiguously free of choicesunambigously gentlemanly.

