Talk:Unary numeral system

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[edit] Unary 8 image

er... the bottom graphic for '8' seems to actually be 9... the tally on the left has 5 vertical bars and 1 horizontal, instead of 4 vertical and 1 horizontal. Someone might want to fix that.

Image:Unary_numeral_eight.png fixed --Henrygb 03:24, 18 Mar 2005 (UTC)
Whoa. I got to this article just as you made that change. It was five when I got the article, and four when I got to the image page. - Vague | Rant 12:51, Mar 18, 2005 (UTC)
Well, judging by the timestamps, I'd say I actually arrived as the cache was being cleared. Same difference. - Vague | Rant 12:52, Mar 18, 2005 (UTC)

[edit] 0 in unary

Am I correct in assuming the unary numeral system is incapable of showing 0? Negative numbers work by putting a minus-sign in front of the digits, just like with any other system, but 0 doesn't seem possible. Of course you'd sort of expect unary's first digit to be the 0, just like every other system's, but that obviously wouldn't work either. :) So, can anyone with the proper knowhow add something sensible about 0 (and negative numbers) to the article? Thanks! Retodon8 18:19, 13 October 2005 (UTC)

This whole page is inaccurate since following the pattern set by other bases (the first digit in the set of available digits being 0) would lead to any unary system equating to zero (0, 00, 000, 0000, ... all equal zero). ThomasWinwood 12:11, 26 October 2005 (UTC)
Yes, that's (part of) what I said, but how does that make this page inaccurate? I'd call it incomplete, because I'd like to see the 0 thing talked about. It does make unary an exceptional base system. Basically it is another symptom for the problem my question was about... how to show the value 0 in unary. I guess it's really as simple as I assumed... it's just not possible. Retodon8 17:35, 26 October 2005 (UTC)

I Don't see why there wouldn't be a zero in unary. 68.118.248.157

Well, I don't know another way to explain. Maybe... try figuring out how you would write zero if you only have the "1" character" (or "|" or whatever), and you'll reach the same conclusion. You can't. You can just not write anything at all, but not having a character for zero disallows a lot of useful stuff in calculations. Retodon8 23:07, 4 January 2006 (UTC)

The thing is, 'the unary numeral system' is a misnomer. It's something that doesn't exist. For any numeral system, you need an origin (zero) and a unit (one). Your 'digits' go from the origin to the number of the base minus one. A number is the summation of each digit times the base to the power of the position of the digit, where the last digit has position zero. So '||||' in unary is 0 * 1^3 + 0 * 1^2 + 0 * 1^1 + 0 * 1^0. Therefore, the smallest possible base is 2. Talking about zero or negative numbers doesn't make sense, because the 'unary' system doesn't make mathematical sense to begin with. SeverityOne 21:06, 6 February 2006 (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. I suggest further discussion of these issues takes place at talk:Non-standard positional numeral systems.--Niels Ø 14:30, 26 February 2006 (UTC)

Unary is not a positional system, even a nonstandard one (though the others you listed are). The "digits" in unary do not depend on position: five tally marks represent the number five, and will still unambiguously represent the number five if you write the same five tally marks in a different order. -- Milo

I initially held the same point of view, but others did consider unary a pos.num.syst., which basically is what made me create the non-std. article. I will now revert your changes; I think the matter should be discussed here first.--Niels Ø 07:41, 2 November 2006 (UTC)
The unary numeral system (base-1, a non-standard positional numeral system) ...

How is unary a positional system? -- Jao 11:43, 27 February 2006 (UTC)

Read the article Non-standard positional numeral systems. One can argue either way, hence non-standard. If you can find an elegant way of putting it, perhaps something like unary, arguably a non-standard positional..., please go ahead and edit accordingly.--Niels Ø 16:52, 27 February 2006 (UTC)
If it is truly "arguably" a positional system, then this is the place to start arguing for it. I have not seen any such arguments, so at the moment the statement is completely unfounded. Incidentally, Non-standard positional numeral systems argues that unary is a non-standard system (which is quite clear), but not that it is a positional system. -- Jao 14:23, 2 November 2006 (UTC)
From Non-standard positional numeral systems:
In a standard positional numeral system, the base b is a positive integer, and b different numerals are used to represent all non-negative integers. Each numeral represents one of the values 0, 1, 2, etc., up to b-1, but the value also depends on the position of the digit in a number. The value of a digit string like d3d2d1d0 in base b is
d_3\times b^3+d_2\times b^2+d_1\times b+d_0.
So what applies to unary, and what not? (Surely, not everything must apply; that's the whole point of considering it a "non-std." system.) The base b=1 is a positive integer; b different numreals are used to represent all non-negative integers (or at least the positive ones; zero only if you allow an null string to represent it); the numeral represents 1 instead b-1=0 as it "should"; the value does not depend on the position, but the equation above applies all the same - because all powers of b are 1. So, many of the standard features do apply, including the equation d_3\times b^3+d_2\times b^2+d_1\times b+d_0, but of course, your objections are caused by the fact that a feature that does not apply is the one implied by the word "position" in the name "positional numeral system". This is a strong argument, but consider that unary undeniably is the bijective numeration system base 1, and all the other bijective numeration systems are positional numeral systems. This proves nothing, but it means that Unary should remain closely linked to Positional numeral system and other related articles. Suppose pos.num.syst.s were called "weighted digit numeration systems" instead (as the digits are assigned weights depending on their position); then we could all agree to include unary as a special case where the weights happen to be all equal.
I suggest we leave unary in the non-std. category, but I also think it's a good idea to mention the doubts one may have about this classification in the article. If unary is not a positional system, it is at least intimately connected to the positional systems, and that must be reflected in our articles. Entirely deleting the section on unary from the article Non-standard positional numeral systems and deleting references to positional systems from Unary is not the way.--Niels Ø 15:00, 2 November 2006 (UTC)

[edit] Unary in theoretical computer science

The article makes out the use of unary in theoretical computer science to be sneaky. I'm sure the reasons unary is used is nothing of the sort. It is used to make formal models of computation manageable. Try writing a Turing machine that multiplies together two numbers given in binary. It is not easy.

Incidentally, in the theory of computation, a modified unary system is often used. In this modified system, "1" means 0, "11" means 1, and so on, so that 0 is representable. CyborgTosser (Only half the battle) 14:04, 17 February 2006 (UTC)

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