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:
“Nothing in the world can take the place of Persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and Determination alone are omnipotent. The slogan “Press On”, has solved and will always solve the problems of the human race.”
—Calvin Coolidge (1872–1933)
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—P.J. (Patrick Jake)