Could I treat this as a closed loop?

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The discussion centers on whether a specific image of an infinitely long bent wire can be considered a closed loop. The initial thought is that it could be treated as such since the ends extend to infinity. However, upon further consideration, the conclusion is reached that it cannot be treated as a closed loop. This highlights the complexity of defining closed loops in mathematical contexts. Ultimately, the consensus is that the wire does not meet the criteria for a closed loop.
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Could I treat this picture as a closed loop? This is part of a much larger problem, so this is all I need to know. I think I can because the ends go off to infinity, but I'm not sure.

http://i.imgur.com/RFCsrqH.jpg
 
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An infinitely long bent wire. Actually, I believe the answer is I can't treat it as a closed loop.
 

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