▁distinct ▁thing ▁which ▁needs ▁to ▁be ▁label led . ▁Non eth eless , ▁of ▁course , ▁sequences ▁of ▁integers ▁may ▁naturally ▁be ▁used ▁as ▁the ▁simplest ▁way ▁to ▁begin ▁lab elling : ▁for ▁example ▁ 1 , ▁ 2 , ▁ 3 ▁and ▁so ▁on . ▁ ▁Definition ▁Al leg edly , ▁the ▁term ▁" nom inal ▁number " ▁is ▁quite ▁recent ▁and ▁of ▁limited ▁use . ▁It ▁appears ▁to ▁have ▁origin ated ▁as ▁used ▁in ▁school ▁text books ▁derived ▁from ▁the ▁statistical ▁term ▁" nom inal ▁data ", ▁alleg edly ▁defined ▁as ▁data ▁indicating ▁"... mer ely ▁statements ▁of ▁qual itative ▁category ▁of ▁membership ." ▁This ▁usage ▁comes ▁from ▁the ▁sense ▁of ▁nom inal ▁as ▁" name ". ▁ ▁Mathemat ically , ▁nom inal ▁number ing ▁is ▁a ▁one - to - one ▁and ▁onto ▁function ▁from ▁a ▁set ▁of ▁objects ▁being ▁named ▁to ▁a ▁set ▁of ▁numer als , ▁which ▁may ▁change ▁( typ ically ▁growing ) ▁over ▁time : ▁it ▁is ▁a ▁function ▁because ▁each ▁object ▁is ▁assigned ▁a ▁single ▁numer al , ▁it ▁is ▁one - to - one ▁because ▁different ▁objects ▁are ▁assigned ▁different ▁numer als , ▁and ▁it ▁is ▁onto ▁because ▁every ▁numer al ▁in ▁the ▁set ▁at ▁a ▁given ▁time ▁has ▁associated ▁with ▁it ▁a ▁single ▁named ▁object . ▁ ▁" N om inal ▁number " ▁can ▁be ▁broad ly ▁defined ▁as ▁" any ▁numer al ▁used ▁for ▁identification , ▁however ▁it ▁was ▁assigned ", ▁or ▁narrow ly ▁as ▁" a ▁numer al ▁with ▁no ▁information