I'm stuck at a problem related to vector space detection. I know how to solve it but don't understand a particular information.
We know that if a set of objects follow 10 axioms of vector space than that defines a vector space.
Say we have a problem:
The set of all positive real numbers with operations
And asked to verify if the set is vector space or not.
Now one of the axioms to be satisfied is:
For each in , there is an object in , called a negative of , such that
For the above problem an object then
Now my question: why's How's that possible? In what way ?
Shouldn't we say that this set is not a vector space because it violates one of the axioms?
I can't seem to find the answer. Can anyone help me on this?