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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the persistence of a number is a term used to describe the number of times one must apply a given operation to an integer before reaching a fixed point, i.e. until further application does not change the number any more. Usually, this refers to the 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, we will assume a radix of 10.