ness ) ▁that ▁are ▁a ▁technical ▁incon ven ience . ▁Element s ▁of ▁B aire ▁space ▁are ▁referred ▁to ▁as ▁" re als ". ▁ ▁V oc ab ul ary ▁and ▁notation ▁▁ ▁Mathemat icians ▁use ▁the ▁symbol ▁R , ▁or , ▁altern atively , ▁ ℝ , ▁the ▁letter ▁" R " ▁in ▁black board ▁bold ▁( encoded ▁in ▁Unicode ▁as ▁), ▁to ▁represent ▁the ▁set ▁of ▁all ▁real ▁numbers . ▁As ▁this ▁set ▁is ▁naturally ▁end owed ▁with ▁the ▁structure ▁of ▁a ▁field , ▁the ▁expression ▁field ▁of ▁real ▁numbers ▁is ▁frequently ▁used ▁when ▁its ▁algebraic ▁properties ▁are ▁under ▁consideration . ▁ ▁The ▁sets ▁of ▁positive ▁real ▁numbers ▁and ▁negative ▁real ▁numbers ▁are ▁often ▁noted ▁R + ▁and ▁R − , ▁respectively ; ▁R + ▁and ▁R − ▁are ▁also ▁used . ▁The ▁non - negative ▁real ▁numbers ▁can ▁be ▁noted ▁R ≥ 0 ▁but ▁one ▁often ▁sees ▁this ▁set ▁noted ▁R + ▁ ∪ ▁{ 0 }. ▁In ▁French ▁mathematics , ▁the ▁positive ▁real ▁numbers ▁and ▁negative ▁real ▁numbers ▁commonly ▁include ▁zero , ▁and ▁these ▁sets ▁are ▁noted ▁respectively ▁ ℝ + ▁and ▁ ℝ − . ▁In ▁this ▁understanding , ▁the ▁respective ▁sets ▁without ▁zero ▁are ▁called ▁strictly ▁positive ▁real ▁numbers ▁and ▁strictly ▁negative ▁real ▁numbers , ▁and ▁are ▁noted ▁ ℝ + * ▁and ▁ ℝ − *. ▁ ▁The ▁notation ▁R n ▁refers ▁to ▁the ▁Cart esian ▁product ▁of ▁n ▁copies ▁of ▁R , ▁which ▁is ▁an ▁n - dimensional ▁vector ▁space ▁over ▁the ▁field ▁of ▁the