Talk:Bijective numeration

message: Considering the Excel example, place value still seems important. Typical decimal symbols could still be used (0-9) and succeed in bijection, (based on what I'm seeing used in the article so) counting 0,1...9,00,01...09,10...19; or 1...9,0,11..19,10,21... This would be useful to add to the article to show the difference between bijective 0-9, 1 thru 0, and decimal 0-9. Phil.andy.graves (talk) 19:36, 25 February 2012 (UTC)
thread_title: Bijective 0-9

message: The terminology "bijective base-k" seems rather misleading, since it suggests that "normal" base-k numeration is not bijective. Our familiar decimal counting system provides a bijection between positive integers and finite-length strings, while "bijective base-10" provides a different bijection. So why do we call it "bijective base-10"? The introduction to this article implies that k-adic numeration is a particularly notable example of bijective numeration, when in fact it seems a comparatively obscure one. Mtford (talk) 21:28, 7 July 2008 (UTC)
replies: text: Looking at the definition again, I notice that ordinary decimal numeration is not bijective if we allow strings beginning with zero (since 1 = 01 = 001, etc.). But it's still bijective over a subset of the possible strings. Intuitively I would say that the difference between "base-10" and "bijective base-10" lies in the definition of the set of strings used to represent numbers, rather than in the property of bijection. Mtford (talk) 22:52, 7 July 2008 (UTC)
replies: text: Yes, the important point is that for bijective numeration there is — as the article states — "a bijection between the set of non-negative integers and the set of finite strings over a finite set of digits".  "Bijective numeration" is the standard term in the literature for this kind of system, even though it is slightly misleading in just the way you mention. r.e.s. (talk) 02:33, 8 July 2008 (UTC)
replies: text: Perhaps the opening paragraph should explain why ordinary numeration (for want of a better term) does not fit the definition, in this case? We should perhaps also mention more explicitly there are only 90 decimal integers of length 2, 900 of length 3, etc, as compared to 100 and 1000 respectively in 10-adic numeration. Mtford (talk) 16:46, 9 July 2008 (UTC)
replies: text: I think your suggestion is a good one, so I gave it a shot.r.e.s. (talk) 19:11, 9 July 2008 (UTC)
thread_title:  Isn't "ordinary" numeration bijective too? 

message: I removed the external link:
*Giovanni Fraterno (Italian)
since it points to a site containing crackpot mathematics.  —Preceding unsigned comment added by 79.53.165.206 (talk) 19:20, 26 February 2009 (UTC)
thread_title:  Link removed 

message: The article has a "citation needed" tag attached to the following statement:
* if k > 1, the number of digits in the bijective base-k numeral representing a nonnegative integer n is \lfloor \log_k (n+1) +\log_k(k - 1) \rfloor
A proof of this statement is given at http://math.stackexchange.com/a/608884/16397. Is this an adequate source for removing the "citation needed" tag? — r.e.s. (talk)  14:14, 22 July 2015 (UTC)
thread_title:  Number of digits in a bijective base-''k'' numeral 

message: The article says a bijective system can represent all non-negative integers. But isn't zero non-negative? I don't see how you could represent zero in this system. Nupanick (talk) 18:42, 14 April 2019 (UTC)
replies: text: Perhaps you missed the first bullet point of the definition section: "The integer zero is represented by the empty string." —David Eppstein (talk) 19:08, 14 April 2019 (UTC)

text: It means a string that has zero characters. You know, like "". —David Eppstein (talk) 15:57, 8 May 2019 (UTC)
thread_title:  Why "Non-negative" and not "Positive"? 

message: It might be worth noting under the examples that the lowest possible base for a bijective numeration system is 1, and that this is the unary numeral system — essentially equivalent to tally marks. 2603:6010:E301:5600:FD08:6942:B377:8E24 (talk) 14:18, 2 September 2022 (UTC)
thread_title:  Unary 

message: Are there any other alphabetic lists aside from the typical one? I’ve seen one that goes A, B, C,… …X, Y, Z, AA, BB, CC,… …XX, YY, ZZ, AAA, BBB, CCC,… 2601:C6:D200:E9B0:B063:CA5:E922:6C9C (talk) 18:56, 7 May 2024 (UTC)
thread_title:  Alternate alphabetic lists