Talk:Positional notation

message: I think it's odd that the issue of fractional numbers is addressed in the section on base-60 but not in base-10. MFH 13:56, 8 Apr 2005 (UTC)
thread_title:  next guy's comment 

message: Also, there is really an important job to do consisting in clearly reorganizing all about base-p, decimal, p-adic, notation vs numbering vs numeral system:
so many things are said about the same thing more or less correctly and more or less contradictionally in so many different places. MFH 13:56, 8 Apr 2005 (UTC)
thread_title:  Reorganize numeral system stuff 

message: I added "place-value notation", a term commonly used in U.S. schools, as a synonym for this type of notation. Based on the description I believe this is accurate, but please someone double-check me. Thanks. Deco 01:58, 6 November 2005 (UTC)
thread_title:  Synonym 

message: I have addressed certain issues by creating the article Non-standard positional numeral systems, and making related changes to Unary numeral system, Golden ratio base, Quater-imaginary base, Positional notation, Base (mathematics), and :Category:Positional numeral systems. Perhaps the reference to the new article in the present article should be in the introduction, as some sort of disambiguation, rather than in the See also section. Apart from that, I suggest further discussion of these issues takes place at talk:Non-standard positional numeral systems.--Niels Ø 14:35, 26 February 2006 (UTC)
thread_title:  Non-standard positional numeral systems 

message: I removed the following paragraph:
The real value of positional notation turned out to be its ability to invite the further study of numbers.  Integers, rational numbers, and place-holders (e.g. zero) were long known about, but irrational numbers, infinity, transfinite numbers, and imaginary numbers were all concepts that could only be discovered once the idea of a continuous number line was implied by positional notation.
''
The concept of infinity and the invention of transfinite numbers are not related to the representation of numbers as points on a line, but is a purely set theoretic idea. Irrational numbers were found as solutions of geometric problems that had no corresponding numeral (rational) representation, long before positional systems came into use (or at least independent thereof).
Hylas 08:51, 20 March 2006 (UTC)
replies: text: I, too, found that paragraph somewhat misleading. On the other hand, the notion of the real number line is an important one, and I think it is far more easily grasped if you have a mental concept of number tied to positional notation. Can this be said in the article in a way that is not misleading?--Niels Ø 11:57, 20 March 2006 (UTC)
replies: text: I added links to the corresponding mathematical ideas. Sadly there is little details provided about the construction. Both articles deal only with the decimal system. Hylas 17:21, 21 March 2006 (UTC)
thread_title:  Mathematical implications 

message: aside: romans did not commonly use the preceding lower order symbol for substraction.  I reckon it would have been more like this:
(plus signs aren't needed now that order means nothing)
IIII XII = XIIIIII = X IIIII I = X V I = XVI
combine, re order, re group
sometimes the process would have to be repeated
--
I retract the earlier complain about the second paragraph being confused, but I still find it confusing. The problem is that it says additive systems are better for arithmetic, but this doesn't seem right at all. Could this be explained? How does positional notation require memorization of tables? Does this mean multiplication tables? Perhaps this matter should be moved out of the article lead. —Preceding unsigned comment added by 24.55.70.103 (talk • contribs) 
:I have serious doubts about that statement too. Roman numerals required the memorization of doubling tables (and possibly other multiplication tables) by everyone taking mathematics in school during the first millennium. Without such memorization the student was not considered competent. Positional notation also requires memorization of multiplication tables. Only when a machine is used (like the abacus) are such tables not needed. — Joe Kress 17:17, 2 June 2006 (UTC)
thread_title:  How is additive system easier for arithmetic? 

message: What the subject says. It can do fractions (most of the time) to a many places, you can make up a base with whatever characters you want as long as each digit is only a single character, it has a list of common bases to choose from when converting. Plus its GNU GPL. I think mine has more features that the other links in this article. The link to my converter is . I tried to add an old version of this long time ago and some admins got all freaky on me and said that it wasn't allowed b/c you had to pay for something... But I'm trying again. Anyway I made it alot faster than my old one b/c its all client side and only requires javascript. Other than that it had all the same features as before. If somebody hosts it on their site and puts a link in the article to their site, I would like it if you would say on the page that you got it from my website. --Deo Favente (talk) 02:43, 20 January 2010 (UTC)
replies: text: HA I added it anyways. Now admins, don't be noobish and say you have to pay for it. I'm still confused about all that. In fact, I'm a huge fan of freedom (libre), and with simple web stuff like this free (gratis) generally comes with. --Deo Favente (talk) 05:37, 23 January 2010 (UTC)
replies: text: I'm sure that nobody wants you to pay to post the website. However, it is generally inappropriate to link to your own website. I looked at the link and your site is rather confusing, you seem to use base not as the numerical base, but as the list of digits. I'm not sure that this site is actually that helpful in it's current form. It would at least help to have some explanation on that page. Cheers, — sligocki (talk) 21:29, 23 January 2010 (UTC)

text: I have not been able to get this link to work any time that I have checked it, even when modifying the link to be ".com" instead of ".com.". If it's not corrected, it should be removed, as it is completely useless if it cannot be accessed. Aleph Infinity (talk) 00:05, 12 February 2010 (UTC)
thread_title:  I want to add my base converter 

message: I think the section Positional notation#Non-standard positional numeral systems should be boiled down to a minimum, with a link to the main article Non-standard positional numeral systems, and with relevant content being merged into that article. Comments?--Nø (talk) 16:59, 13 June 2010 (UTC)
thread_title:  Non-standard positional numeral systems (2) 

message: Please see Category talk:Positional numeral systems#List of positional systems by base.--Nø (talk) 10:55, 24 October 2010 (UTC)
thread_title:  List of positional systems by base 

message: I carried this paragraph in the article "Complex Base Systems"--Solikkh (talk) 13:27, 26 April 2011 (UTC)
thread_title:  Complex radixes 

message: --Solikkh (talk) 18:53, 24 April 2011 (UTC)
thread_title: References

message: "It was likely motivated by counting with the ten fingers. "  Lol.  Maybe, but you'd need to chop off a finger or count one of them as zero.  Is there much research into the history of the base ten number system?  — Preceding unsigned comment added by 96.33.158.121 (talk) 04:53, 12 September 2011 (UTC)
thread_title: It was likely motivated by counting with the ten fingers. 

message: A section titled "Exponentiation" where the images display how the digits are laid out, is there a way I can have consistent font so I can edit the image to display parenthesis like this (or simply have them in text):
 2506 = (2 * b3) + (5 * b2) + (0 * b1) + (6 * b0)
Because some users might do the formula in the incorrect order.
Also for mentioning different radixes/bases such as where “In base-16 (hexadecimal), there are 16 hexadecimal digits (0–9 and A–F) and the number” is mentioned, it can confused some users because using symbols 0-9 looks like decimal, when they could be hex numbers. I think it would be better to use subscript, for example: 1010 = A16
Please let me know what you think.
97.83.63.211 (talk) 23:07, 2 March 2018 (UTC)
replies: text: I've implemented your first suggestion.  Mathematically there is no need, but using the parenthesis does enforce what is happening to a student.  In the second case though I can't see where the ambiguity arises, unless you are suggesting not using the universal convention that the digits 0-9 retain their meaning in all systems in which they are present.  Subscripts work here where the text is processed, but are useless when computer sources are seen.  Consider: 1234567 = 4553207 = 12d687.  The last form is unambiguous, the first two can be confused.  Martin of Sheffield (talk) 11:27, 3 March 2018 (UTC)
thread_title:  a note for Exponentiation 

message: From § Issues:
In the example of Chinese usage provided, 壹佰 (100) is contained within 伍仟壹佰 (5100).  Given that the characters "伍仟" can be inserted at the beginning to change the value, how does writing out the number on a check in Chinese prevent fraud (in this instance, at least)?
Technotom2001 (talk) 19:56, 13 December 2018 (UTC)
thread_title:  Issues: Susceptibility to fraud in Chinese 

message: A citation needs to be given to a reliable source proposing  this. Peter Brown (talk) 01:57, 24 September 2020 (UTC)
replies: text: If you mean Positional digits alternating in sign, then there is now given: E.g. Knuth. –Nomen4Omen (talk) 09:12, 24 September 2020 (UTC)
thread_title:  Positional factors alternating in sign: Original research?