Editing Numerical digit (section)

==Digits in mathematics==
Despite the essential role of digits in describing numbers, they are relatively unimportant to modern [[mathematics]].<ref>{{Cite web|last=Kirillov|first=A.A.|title=What are numbers?|url=https://www.math.upenn.edu/~kirillov/MATH480-S08/WN1.pdf|website=math.upenn.|page=2|quote=True, if you open a modern mathematical journal and try to read any article, it is very probable that you will see no numbers at all.}}</ref> Nevertheless, there are a few important mathematical concepts that make use of the representation of a number as a sequence of digits.

===Digital roots===
{{main|Digital root}}
The digital root is the single-digit number obtained by summing the digits of a given number, then summing the digits of the result, and so on until a single-digit number is obtained.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Digital Root|url=https://mathworld.wolfram.com/DigitalRoot.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref>

===Casting out nines===
{{main|Casting out nines}}
[[Casting out nines]] is a procedure for checking arithmetic done by hand. To describe it, let <math>f(x)</math> represent the [[digital root]] of <math>x</math>, as described above. Casting out nines makes use of the fact that if <math>A + B = C</math>, then <math>f(f(A) + f(B)) = f(C)</math>. In the process of casting out nines, both sides of the latter [[equation]] are computed, and if they are not equal, the original addition must have been faulty.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Casting Out Nines|url=https://mathworld.wolfram.com/CastingOutNines.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref>

===Repunits and repdigits===
{{main|Repunit}}
Repunits are integers that are represented with only the digit 1. For example, 1111 (one thousand, one hundred and eleven) is a repunit. [[Repdigit]]s are a generalization of repunits; they are integers represented by repeated instances of the same digit. For example, 333 is a repdigit. The [[prime number|primality]] of repunits is of interest to mathematicians.<ref>{{MathWorld|urlname=Repunit|title=Repunit}}</ref>

===Palindromic numbers and Lychrel numbers===
{{main|Palindromic number}}
Palindromic numbers are numbers that read the same when their digits are reversed.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Palindromic Number|url=https://mathworld.wolfram.com/PalindromicNumber.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref> A [[Lychrel number]] is a positive integer that never yields a palindromic number when subjected to the iterative process of being added to itself with digits reversed.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Lychrel Number|url=https://mathworld.wolfram.com/LychrelNumber.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref> The question of whether there are any Lychrel numbers in base&nbsp;10 is an open problem in [[recreational mathematics]]; the smallest candidate is [[196 (number)|196]].<ref>{{Cite book|last1=Garcia|first1=Stephan Ramon|url=https://books.google.com/books?id=7qCdDwAAQBAJ&q=Lychrel+196&pg=PA104|title=100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection|last2=Miller|first2=Steven J.|date=2019-06-13|publisher=American Mathematical Soc.|isbn=978-1-4704-3652-0|pages=104–105|language=en}}</ref>