Answer
$yes\,\left \{ \mathbb{R^{+}},\mathbb{R^{-}},\left \{ 0 \right \} \right \}\,\,is\,a\,partition\,of\,\mathbb{R}$
Work Step by Step
$any\,\,real\,\,number\,\,can\,\,either\,\,be\,\,zero\,\,or\,positve\,number\,or\,\,negative\,\,number$
$so\,\,\mathbb{R^{+}}\cup \mathbb{R^{-}}\cup \left \{ 0 \right \}=\mathbb{R}$
$and\,\,{R^{+}} ,{R^{-}} ,\left \{ 0 \right \} are\,mutually\,\,disjoint(as\,\,\mathbb{R^{^{+}}}\cap \mathbb{R^{-}}=\varnothing ,\,\,\,\,\mathbb{R}^{+}\cap\left \{ 0 \right \}=\varnothing,\mathbb{R}^{-}\cap\left \{ 0 \right \}=\varnothing )$
$so\,\,\left \{ \mathbb{R^{+}},\mathbb{R^{-}},\left \{ 0 \right \} \right \}\,\,is\,a\,partition\,of\,\mathbb{R}$
