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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-dimensional?

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

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

Question. Is there a gentlemanly way to prove that the natural map from $V$ to $V^{**}$ is surjective if $V$ is finite-dimensional?

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

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-dimensional?

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

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-dimensional?

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

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.

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-dimensional?

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