Narcissistic Decimals

We consider a collection of variations on the classic definition of the Narcissistic Numbers. Each new definition is tied to decimals found in the unit interval. The first definition, Narcissistic Decimals, is shown to be connected to the Perfect Digital Invariants and presents a new approach of the question of the cardinality of that set. Another definition, Ascending Narcissistic Decimals, produces a Cantor set. A third definition, Descending Narcissistic Decimals, produces a challenging set with a small number of interesting examples.