▁to ▁be ▁a ▁logical ▁conj unction ▁because ▁of ▁the ▁repeated ▁use ▁of ▁" and ". ▁However , ▁the ▁" etc ." ▁cannot ▁be ▁interpreted ▁as ▁a ▁conj unction ▁in ▁formal ▁logic . ▁Instead , ▁the ▁statement ▁must ▁be ▁re phr ased : ▁For ▁all ▁natural ▁numbers ▁n , ▁ 2 · n ▁= ▁n ▁+ ▁n . ▁This ▁is ▁a ▁single ▁statement ▁using ▁universal ▁quant ification . ▁ ▁This ▁statement ▁can ▁be ▁said ▁to ▁be ▁more ▁precise ▁than ▁the ▁original ▁one . ▁While ▁the ▁" etc ." ▁inform ally ▁includes ▁natural ▁numbers , ▁and ▁nothing ▁more , ▁this ▁was ▁not ▁rig or ously ▁given . ▁In ▁the ▁universal ▁quant ification , ▁on ▁the ▁other ▁hand , ▁the ▁natural ▁numbers ▁are ▁mentioned ▁explicitly . ▁ ▁This ▁particular ▁example ▁is ▁true , ▁because ▁any ▁natural ▁number ▁could ▁be ▁subst it uted ▁for ▁n ▁and ▁the ▁statement ▁" 2 · n ▁= ▁n ▁+ ▁n " ▁would ▁be ▁true . ▁In ▁contrast , ▁For ▁all ▁natural ▁numbers ▁n , ▁ 2 · n ▁> ▁ 2 ▁+ ▁n ▁is ▁false , ▁because ▁if ▁n ▁is ▁subst it uted ▁with , ▁for ▁instance , ▁ 1 , ▁the ▁statement ▁" 2 · 1 ▁> ▁ 2 ▁+ ▁ 1 " ▁is ▁false . ▁It ▁is ▁imm aterial ▁that ▁" 2 · n ▁> ▁ 2 ▁+ ▁n " ▁is ▁true ▁for ▁most ▁natural ▁numbers ▁n : ▁even ▁the ▁existence ▁of ▁a ▁single ▁counter example ▁is ▁enough ▁to ▁prove ▁the ▁universal ▁quant ification ▁false . ▁ ▁On ▁the