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A theorem in mathematics is the statement that has been proved it van be proved to be true.
Your information is incomplete. Therefore, an overview will be given. A theorem simply means a statement that can be demonstrated to be true based in mathematical proportions and arguments.
A vector space is simply the set of objects called vectors that can be added together and multiplied by numbers that are called scalars. An example is a² + b² = c² for a right angled triangle.
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