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Why these statements are not mathematically equivalent?

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- Thread starter Cozma Alex
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- #1

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Why these statements are not mathematically equivalent?

- #2

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https://en.wikipedia.org/wiki/Conservative_force#Mathematical_description

is inaccurate (mathematically spoken it's simply wrong). The Wikipedia author(s) forgot that the Poincare lemma is valid only in simply-connected regions of space. The most famous counter example is the potential vortex. See here:

https://www.physicsforums.com/threads/struggling-with-ab-effect.872156/#post-5477281

- #3

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https://en.wikipedia.org/wiki/Conservative_force#Mathematical_description

is inaccurate (mathematically spoken it's simply wrong). The Wikipedia author(s) forgot that the Poincare lemma is valid only in simply-connected regions of space. The most famous counter example is the potential vortex. See here:

https://www.physicsforums.com/threads/struggling-with-ab-effect.872156/#post-5477281

Thanks!

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