is there such a thing as an infinitely repeated digit in an integer

Asked May 07 '20 at 14:28

Active May 07 '20 at 14:28

Viewed 24 times

Is there such a thing as an infinitely repeated digit in an integer?

Analogous to how there are repeating or recurring decimals.

If there is what do you call them(if they indeed have a name)? If not why?

For example, I mean numbers like:

$...999999999, ...4444444412, ...11111111, etc.$

I tried looking up "infinitely repeated digit in an integer" and similar things on Google but I got nothing for whatever reason. Surely, I couldn't have been the first person to think about this, no?

asked May 07 '20 at 14:28

My mistake

1

Welcome to Mathematics Stack Exchange. Not in regular integers, but read about p-adic numbers – J. W. Tanner May 07 '20 at 14:30
No such integers does not satisfy Archimedean property – user12986714 May 07 '20 at 14:31
1

@J.W.Tanner At this point, p-adic numbers are a bit over my head but I'm hoping to work towards them anyway. They seem interesting. P.S — Do you know the term for the type of numbers I just described? – My mistake May 07 '20 at 14:46
@user12986714 This is a property of some system of numbers and therefore does not hold in others, right? – My mistake May 07 '20 at 14:49
Assuming that you are talking about the ordinary decimal representation of integers, the answer is no. For example, your $...111111$ is an abbreviation for $\sum_{n\ge 0}10^n$, which is a divergent series and therefore does not represent any integer. – Brian M. Scott May 07 '20 at 15:09
@BrianM.Scott Oh, ok. Thanks that makes sense. – My mistake May 07 '20 at 15:11
@Mymistake: You’re welcome. – Brian M. Scott May 07 '20 at 15:16
Yes. Yet integers in this context, if referring to some "normal" real numbers, need to satisfy that property – user12986714 May 07 '20 at 15:18

is there such a thing as an infinitely repeated digit in an integer

0 Answers0