- #1

- 699

- 5

Define the operation of scalar multiplication, denoted ∘, by α∘x = x^α, x ϵ ℝ+ and α ϵ ℝ.

Define the operation of addition, denoted ⊕, by x ⊕ y = x·y, x, y ϵ ℝ+.

Thus, for this system, the scalar product of -3 times 1/2 is given by:

-3∘1/2 = (1/2)^-3 = 8 and the sum of 2 and 5 is given by:

2 ⊕ 5 = 2·5 = 10.

Is ℝ+ a vector space with these operations? Prove your answer.

6. (α ⊕ β)∘x = x^(α ⊕ β) = x^(α·β) = x^(β·α)

Am on the right path for this axiom?