Question

is "R+" is subspace of "R"..?Why?

Answer 1

A vector subspace?

Answer 2

yes

Answer 3

Subspaces must satisfy a number of axioms. R^+ doesn't satisfy all of them and isn't a subspace. In particular, given any vector
\[ x \in \mathbb{R}^+ \]
there should be another vector \[ y \in \mathbb{R}^+ \] such that
\[ x + y = 0 \]
But this is clearly not the case.

Answer 4

E.g., x = 1. The additive inverse vector, y, would be y = -1. But -1 isn't in R^+

Answer 5

Thank you JamesJ , by the example it become clearly.