I Proving Vector Space of Circles is Not Axiomatic

mikeeey
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Hi
How can i prove that the set if circles does not form a vector space AXIOMATICALLY .
( i am not considering a circle lives in xy-plane ( subset ) as a subspace of xy-plane
 
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Could you check your post and perhaps re-formulate it in correct sentences so that it becomes understandable? Thank you.
 
Hey mikeeey.

You will need to define your addition and scalar multiplication operators and then check the usual 10 axioms.
 

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