In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more.
Usually, this involves additive or multiplicative persistence of an integer, which is how often one has to replace the number by the sum or product of its digits until one reaches a single digit. Because the numbers are broken down into their digits, the additive or multiplicative persistence depends on the radix. In the remaining article, base ten is assumed.
The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence is the measure of how many times we must sum the digits it takes us to arrive at its digital root.
Read more about Persistence Of A Number: Examples, Smallest Numbers of A Given Persistence
Famous quotes containing the words persistence and/or number:
“Extreme patience and persistence are required,
Yet everybody succeeds at this before being handed
The surprise box lunch of the rest of his life.”
—John Ashbery (b. 1927)
“The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.”
—Anton Pavlovich Chekhov (1860–1904)