14-240/Tutorial-October7

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Boris

Subtle Problems in Proofs

Check out these proofs:

(1) Let , be subspaces of a vector space . We show that is a subspace .

Assume that is a subspace.
Let .
Then and .
Then .
Case 1: :
Since and has additive inverses, then .
Then .
Case 2: :
Since and has additive inverses, then .
Then .
Then .
Then . Q.E.D.


(2) Let . Then , define and . We show that is not a vector space over .

Nikita