Transfinite sequence

of elements of a given set $ X $

A mapping of an interval $ [ 0, \beta ) $ of (transfinite) ordinal numbers into $ X $( cf. also Ordinal number). By an element, or term, of the transfinite sequence $ f: [ 0, \beta ) \rightarrow X $ is meant an ordered pair $ ( \alpha , x) $, where $ \alpha \in [ 0, \beta ) $ and $ x= f( \alpha ) $; this term is often denoted by $ x _ \alpha $.