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I'm reading Conway's complex analysis book and on page 64 the author has enunciated the following definition:

However, on page 81 the author has stated that:

I think Conway was mistaken in the first definition. If I remember well from my algebraic topology classes, the second definition is the true definition of $\gamma^{-1}$.

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    $\begingroup$ "This is actually a reparametrization of the original definition”. $\endgroup$ – egreg Feb 9 '16 at 22:30
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    $\begingroup$ As egreg points out, he notes the change himself. Also, the original isn't given as a formal definition, just a notation for the theorem that follows it, which is about properties of the integral, not homotopy. $\endgroup$ – Paul Sinclair Feb 10 '16 at 0:44

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