Let V denote the set of positive real numbers. Define the operation of scalar multiplication, denoted —¦, by
α —¦ x = xα
for each x ˆŠ R+ and for any real number a. Define the operation of addition, denoted Š•, by
x Š• y = x ˆ™ y for all x, y ˆŠ R+
Thus for this system the scalar product of - 3 times 1/2 is given by

and the sum of 2 and 5 is given by
2 Š• 5 = 2 ˆ™ 5 = 10
Is R+ a vector space with these operations? Prove your answer.

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