amolv06
Feb25-08, 06:26 PM
1. The problem statement, all variables and given/known data
Let R denote the set of real numbers. Define scalar multiplication by \alpha x = \alpha x which is simply regular scalar multiplication, and vector addition is defined as x \oplus y = max(x,y). Is R a vector space with these operations?
2. Relevant equations
Some given above.
3. The attempt at a solution
There seems to be no zero vector to this equation as for any number k there exists another number k-1, so there is no single 0 vector for a vector space with the operations defined above. Is this reasoning correct?
Let R denote the set of real numbers. Define scalar multiplication by \alpha x = \alpha x which is simply regular scalar multiplication, and vector addition is defined as x \oplus y = max(x,y). Is R a vector space with these operations?
2. Relevant equations
Some given above.
3. The attempt at a solution
There seems to be no zero vector to this equation as for any number k there exists another number k-1, so there is no single 0 vector for a vector space with the operations defined above. Is this reasoning correct?