Talk:Positional notation

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[edit] next guy's comment

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)== Fractional numbers ==

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)

[edit] Reorganize numeral system stuff

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)

[edit] Synonym

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)

[edit] Non-standard positional numeral systems

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)

[edit] Mathematical implications

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)

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)
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)

[edit] How is additive system easier for arithmetic?

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.[1] 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)

For simple addition and subtraction, the Roman numeral system is basically abacus-like; so for instance

IV + XII = V + XI = VI + X = XVI

This isn't the actual computation someone would perform, but rather an attempt to replicate the abstract process the user of Roman numerals might engage in to perform an addition. For basic monetary transactions, it is slightly faster.