Proving Vector Space of Circles is Not Axiomatic

mikeeey · Aug 8, 2016

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

S.G. Janssens · Aug 8, 2016

Could you check your post and perhaps re-formulate it in correct sentences so that it becomes understandable? Thank you.

chiro · Aug 9, 2016

Hey mikeeey.

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

Proving Vector Space of Circles is Not Axiomatic

Discussion

Similar threads

Undergrad A few questions about proving vector spaces

Proving Vector Subspace $U \notin R^3$

Undergrad Proving vectors are in the column space

Graduate Proving Vector Space Relationships in WU{A} and WU{B}

Graduate Proving Vector Space of F[x]/(g(x)) with Degree n

Proving Vector Space Property: αa = 0 ⟹ α = 0 or a = 0

Proving Vector Space Axioms for f(x) = ax+b, a,b Real Numbers

Undergrad Proving Vector Subspace: V in W iff V+W in W

Proving Vector Space of R^2: Solving Question and Finding Zero Vector

Proving Vector Space Properties for a Set of Scalar Multiples of [1,3,2] in R3