Graduate Bachman : A geometric approach to differential forms

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In Bachman's book, the expression for a vector in the tangent space is presented as dx(0,1) + dy(1,0), which raises questions about its correctness. The discussion clarifies that the notation reflects a specific convention in differential geometry, where the order of differentials matters. The alternative expression, dx(1,0) + dy(0,1), does not align with the established conventions for representing tangent vectors. Participants emphasize the importance of understanding these conventions to avoid confusion. Overall, the notation is not a typo but rather a deliberate choice based on geometric principles.
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Forms and basis in TpC (page 18)
Hi All!
First of all , sorry for my English :)
In Bachman's book, on page 18, a vector in the tangent space is written in the form dx(0,1)+dy(1,0). Why is it not written the other way around, so why isn’t dx(1,0)+dy(0,1) the correct expression? Thank you.
 
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It looks like a typo.
 
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