# Vector Space question

1. Feb 25, 2008

### amolv06

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?

2. Feb 25, 2008

### HallsofIvy

Staff Emeritus