# When denoting a utility function in terms of real numbers R, what does the plus in subscript denote?

So, we can see that for the below question, we are asked to show linear demand for a utility function $(\mathbb{R}^n)_+ \to \mathbb{R}$. My question is, what does the plus symbol in the set R represent? I am seeing this notation across several real number sets, but do not know what it stands for.

• Typically, $\mathbb{R}^n_+$ is used to denote either the positive or the non-negative $2^n$-thant of the euclidean space. Whether it's the former or latter is more a matter of convention than anything else, and you should look for previous usage to determine which, although it may not make much of a difference for this particular example. – stochasticboy321 Nov 1 '15 at 22:12
• @stochasticboy321 Since $\alpha=0$ is allowed above, I'm inclined to think it's the non-negative version. Also, your comment could be an answer. – user147263 Nov 1 '15 at 22:14