I am trying to prove that a set V is a vector space, I managed to prove most of the process, but stuck with a couple of things...
The set V is the set of positive real numbers, and the field is R.
the two operations are:
x++y = xy
a**x = x^a
(where ++ is the addition, ** is the scalar multiplication, and a is a real scalar)
I find it hard to prove that for 2 scalars r and s, and a member of V, x
(r++s)**x = (r**x) + (s**x)
basically what I don't understand, is what do to when having
r**s, in other words, when I have to multiply 2 scalars, do I do it using the regular operator, or using the new X*scalar operator
any help would be appreciated...