Talk:Non-integer base of numeration

This article was nominated for deletion on 11 November 2009. The result of the discussion was keep.

The idea of base 0.1 is not valid. Any base system must use numerals that are less than the base under consideration. The article makes the assertion that using numerals 0 through 9 is okay for a base that is smaller than 1. There is no other source I can find for this numeral system. HumphreyW (talk) 12:06, 22 August 2009 (UTC)[reply]

It has been a week and no one else seems to be concerned about it either way so I am going to remove the unsourced text from the article. HumphreyW (talk) 02:49, 29 August 2009 (UTC)[reply]

There's no golden rule that says that you can only uses numerals that are less than the base being used; in general, the rule is that you have to use all of the numerals needed before another column can start to be filled. With base 0.1 it takes 10 1's before another column starts to fill (the 10's) and it takes 10 0.1's before a 1 can jump into the 1's column, so the base has to use 10 symbols. With base 0.125 it takes 8 1's before a 1 goes into the 8's column so there are 8 symbols used, and in general we can say that if the base is less than 1 then with base 1/x x numerals are used. Robo37 (talk) 13:40, 20 September 2009 (UTC)[reply]

I think it is better to stick with the convention that most sources adopt, that β > 1 and that the coefficients in the expansion are nonnegative integers less than β. It would be very difficult to structure a coherent article otherwise. Other conventions, if they can be sourced, perhaps belong in a dedicated section towards the end. Le Docteur (talk) 00:52, 12 November 2009 (UTC)[reply]