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 at which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative 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 remainder of this article, base ten is assumed.
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| - Persistance d'un nombre (fr)
- Persistenza di un numero (it)
- Persistence of a number (en)
- 数的韧性 (zh)
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| - La persistance d'un nombre est, en mathématiques, le nombre d'étapes nécessaires pour atteindre un point fixe, lorsqu'on effectue par itérations successives une série d'opérations à ce nombre. (fr)
- 数的韧性是針對正整數的特性，是指此整數需連續進行幾次特定的處理才能到達不動點，數字不再變動。 数的韧性一般可分為加法韧性及乘法韧性，前者是反覆針對數字的各位數字求和（即數字和），後者則是反覆計算各位數字的乘積，當數字為1位數時即為不動點，數字不會再變動。因為結果會依各位數字的有所不同，数的韧性也和進制有關，以下只考慮十進制的情形求和。 當反覆計算數字和時，最後的不動點即為該數字的數字根。因此一數字的加法韧性也可以定義為一數字需計算幾次數字和才能得到其數字根。 (zh)
- 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 at which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative 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 remainder of this article, base ten is assumed. (en)
- In matematica, la persistenza di un numero è il termine usato per descrivere il numero di operazioni che si devono applicare ad un intero per raggiungere un punto fisso, ad esempio fino a quando successive operazioni non cambieranno più il numero. (it)
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| - 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 at which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative 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 remainder of this 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 counts how many times we must sum its digits to arrive at its digital root. (en)
- La persistance d'un nombre est, en mathématiques, le nombre d'étapes nécessaires pour atteindre un point fixe, lorsqu'on effectue par itérations successives une série d'opérations à ce nombre. (fr)
- In matematica, la persistenza di un numero è il termine usato per descrivere il numero di operazioni che si devono applicare ad un intero per raggiungere un punto fisso, ad esempio fino a quando successive operazioni non cambieranno più il numero. Generalmente, questo termine viene riferito alla persistenza additiva o moltiplicativa di un intero, che indica quante volte bisogna sostituire un numero con la somma o con la moltiplicazione delle sue cifre fino a quando si raggiunge un numero con una sola cifra.La persistenza additiva o moltiplicativa dipende dalla base di numerazione in cui si sta operando. In quest'articolo si considerano solamente i casi in base 10. (it)
- 数的韧性是針對正整數的特性，是指此整數需連續進行幾次特定的處理才能到達不動點，數字不再變動。 数的韧性一般可分為加法韧性及乘法韧性，前者是反覆針對數字的各位數字求和（即數字和），後者則是反覆計算各位數字的乘積，當數字為1位數時即為不動點，數字不會再變動。因為結果會依各位數字的有所不同，数的韧性也和進制有關，以下只考慮十進制的情形求和。 當反覆計算數字和時，最後的不動點即為該數字的數字根。因此一數字的加法韧性也可以定義為一數字需計算幾次數字和才能得到其數字根。 (zh)
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