Question Number 1537 by 2closedStringsMeet last updated on 17/Aug/15
$${Show}\:{by}\:{use}\:{of}\:{the}\:{characteristics}\:{of} \\ $$$${a}\:{vector}−{space},\:{that}\:{the}\:{set}\:\overset{\rightarrow} {{x}}\in\mathbb{R}_{+} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{following}\:\mathrm{operations}\:\oplus\:{and}\: \\ $$$${builds}\:{a}\:{vector}−{space}. \\ $$$$\ast{Use}\:{vector}−{space}\:{axioms} \\ $$$$\ast\overset{\rightarrow} {{x}}\oplus\overset{\rightarrow} {{y}}\:\:\:\:{be}\:\:\:\overset{\rightarrow} {{x}}\centerdot\overset{\rightarrow} {{y}} \\ $$$$\ast{for}\:\lambda\in\mathbb{R}\:\:{set}\:\:\lambda \overset{\rightarrow} {{x}}\:\:{equal}\:\overset{\rightarrow\lambda} {{x}} \\ $$