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Pages: (2) 1 [2]  ( Go to first unread post )

 Difference Btwn Base, Radix, Numeral/number System
wendy.krieger
Posted: Apr 4 2016, 09:24 AM


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Pinbacker's question is cached in a form that there is some Académe Scientifique which dictates usage in the way the french academe does the language. This is not so. In fact, much of the modern terminology can not be traced back past WW2.

The scalar and vector products are written in Heaviside (1898) as Sab and Vab respectively, and in Lorentz (1916) as (a,b ) and [a,b]. We write these as \(a\cdot b\) and \( a\times b\). More recently, where Coxeter writes \( t_{a,b,c}\{3,3,5\}\), John Conway writes \( a_{a,b,c}\{3,3,5\}\). These of course, derive from Mrs Stott's notation, which is \( e_{a,b,c}C_{600}\). It makes a whole lot of sense when one is confrunted with with \( t_2 \{3,3,5\} \) as it is not perfectly clear to what the 2 refers to, and even if you figure it out, you have to realise the count begins at zero. So my form is o3o3x5o. You count from the left, 0,1,2. But we can write different values for x. Richard Klitzing has a zoo that runs through all the letters and now we're into separate upper case examples. Dear dear me.

The closest I find to base-n terminology is they simply it's the same for base-10, but upped and down to base-x. The problems occupy about a week in grade-six here, and something similar in university. This is why I call it decim. There is no need for a specific word for the terminology if that's all there is.

The implications of decim use is that if it's used in science, it must be right, and we can apply it to any base, and we see that Icarus is inventing runes for digits as far as one wants, and that Kode is talking of "subdigits" (a term i have never heard elsewhere). We have people churning out techneques to multiply these runes or their decimal encodings, as if we were looking at a big ten.

This is because Kode is tieing the word 'digit' to the decim abstraction of 'place-value', and finding several numerals in each 'digit', supposes that these must be subdigits. On the other hand, i tie 'digit' to 'numeral-place', and then a decim-abstraction digit is actually a place of two digits. See examples of this with the words 'face', 'cell', in the polygloss, where different root-meanings of the same word become competing meanings in the art.

People who speak more than one language will appreaciate that words have little meaning-points that translate to different words in their language. So we have the word 'early', actually has sub-meanings of 'early for', 'early to', and 'early in', an early bloomer is an 'early to fruit', and early-to is not a word you use for early-for the train. Yet we see scientists take an english word 'boundless', and derive 'apeiron' in greek, and suppose that this can be used of number. Apeiron is boundless in space, like the open sea or desert.

Twelfty is not read as a decim base. That's why i invented a distinction of terminologies, with centim as a new branch. You don't get anywhere by pretending that 40 and 60 and 120 are just big decimal bases. The historical records show that these are alternating symbols of 4, 6, 12 and 10. When we cut the digit-set to ten or twelve, we can still deal with these big bases, but we need to sever ties with decim thinking, and think differently. I invented words like 'staff' and 'twistaff', because the word 'digit' maps onto two different points in twelfty, one occupied by one staff or character, and the other occupied by two. But Kode seemed to objected to this construct.

Centim calculations and thinking is not in the standard arithmetics or in the number theories. I searched all the literature available for clues. Even those who mentioned 30 and 60 as bases, were at a loss to how to calculate in these bases. Gardner gave no clues, concluding 30 was too big. Neugebauer said he used the Sumerian ready reckoners to do the calculations. When you read Neugebauer with an understanding of the centim structure, you see different things than when you suppose it's a large decim base. So alternating arithmetic really and truly is cutting edge research.

Kode suggests that I push an agenda, and get upset if people don't use my way. This is not the truth. I simply push the outcome of 30 years of study in the subject. It really does not matter one way or the other if other people accept or reject it: i should none the less be able to opine on the subject and my experience with it.

Kode picks on the stilted form 'one should ...' but fails to note that using 'we should ..' is the current replacement for it. It's presented as the 'royal we' etc. However, it is not an uncommon construction, and this is the reason that I suggested that Kode is from a non-english-speaking background. He has poked exactly the same accusation at me. In my opinion, 'one should ..' is fairly legitimate, and translate german 'man' for one, in this case.

The reason that I reject quantitels as unit-names are exactly the same ones that they have been rejected in the 1860s, and ever since. The use of quantitels supposes that everyone is following ISO 31, and that any other thinking is necessarily muddled. Kode even goes as far as to suggest that people who invented quantities in terms of the theories and units of 1830, are somehow muddling up the units and dimensions of 1947, and that the older people should had known better. So if the people who wrote the 1947 tomes are muddling up those who wrote the 2066 ones?

In practice, dimensional analysis is not about what's in ISO 31, but a lengthy art in describing scaling rules for experimental data on unknown formulae. There are weighty tomes running to thousands of pages, and the likes of Rayleigh's process and Buckingham's \(\pi\) theorm. Sir Graham Taylor annoyed the hell out of the americans by calculating the explosive forces of their atom bomb simply from photographic material. This was done by dimensional analysis, and not the sort of ISO 31 quantitel nonsense.
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Kodegadulo
Posted: Apr 4 2016, 11:30 AM


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QUOTE (wendy.krieger @ Apr 4 2016, 09:24 AM)
The use of quantitels supposes that everyone is following ISO 31,

Hmm. I wasn't familiar with the existence of ISO 31, but since it's something that Wendy considers "nonsense", there are probably some good ideas in it. And, sure enough, it turns out they coined:

New phrase Existing phrase Technical meaning
massic quantity specific quantity a quantity divided by its associated mass
volumetric quantity [volumic] quantity density a quantity divided by its associated volume
areic quantity surface quantity density a quantity divided by its associated area
lineic quantity linear quantity density a quantity divided by its associated length


So a synonym for "densitel" could be "volumic-massel". Its inverse could be "massic-volumel" as a unit of specific volume. A synonym for "pressurel" could be "areic-forcel". A synonym for "energy-densitel" could be "volumic-energiel". Instead of being confused over what a "charge-densitel" might mean, we could distinguish "lineic-chargel" vs "areic-chargel" vs "volumic-chargel".

Yes, this is very helpful in enhancing Quantitels. And since it's an ISO standard, it will be well understood by current physicists.

But this exchange has been completely off topic of Pinbacker's original question.
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Kodegadulo
Posted: Apr 4 2016, 11:48 AM


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QUOTE (wendy.krieger @ Apr 4 2016, 09:24 AM)
Kode even goes as far as to suggest that people who invented quantities in terms of the theories and units of 1830, are somehow muddling up the units and dimensions of 1947, and that the older people should had known better. So if the people who wrote the 1947 tomes are muddling up those who wrote the 2066 ones?

I would never fault people of an earlier era for being ignorant of knowledge acquired in a later era. I would only fault someone who today insists on perpetuating the thinking of earlier eras, even though we know better now.
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wendy.krieger
Posted: Apr 4 2016, 11:56 AM


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The point is that Pinbacker's question is asking about 'modern science' terminology for these things. Modern science does not spend a lot on base words, and all they do is filter in words from common language, and try to extend them.

My point is that the question has no difinitive answer, and even if it did, it's only some one else's opinion based on their view of things.

The words that describe Pinbaker's words are then 'numeral' and 'digit' as in common use. A number is comprised of numerals, but you talk of any of its various lengths as so many digits. So 1234 is a four-digit number, and 12.34 is also a four digit number or 'one point one digits' by logrithmic calculations.

Digit means finger, and supposedly the ten digits mean the ten numerals.

Twelfty uses a different paradigm, and \digit\ is replaced by a number of different words, because digit covers quite different meanings which are exposed in twelfty. So you have place / staff / twistaff, but if a digit is a place on the counting board, and column carries are preserved, there are also rows. But Kode does not like that terminology, so we're not allowed to discuss it.

ISO 31

ISO 31 represents the latest thinking in quantities, but it is not without errors. Physicists themselves do not use this, but annotated extracts of it.

But I don't think it is 'nonsense'. I used it as the base to develop the full map of dimensions in use, and supplemented it with other units, such as found searching through the likes of Weast's "rubber bible" (Ed. 60: CRC Handbook of Physics and Chemistry). The zoo is still maintained, recent entries include permeability (T/L) [Shircz], poricity ('darcy').

What I think is nonsense is that quantities have a single point, and that such might be listed in something like ISO 31.

Lorentz-Heaviside

Once you have a general six-dimensional theory, LHU is simply set \( \beta = \eta = 1, \qquad \kappa = c \) which is rules GR, and you get LHU. Buying the books on it was simply to see if this were right. It's simply a triple-fold on the general theory.
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Kodegadulo
Posted: Apr 4 2016, 12:13 PM


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QUOTE (wendy.krieger @ Apr 4 2016, 09:24 AM)
Pinbacker's question is cached in a form that there is some Académe Scientifique which dictates usage in the way the french academe does the language.

I didn't get that impression, but I'm sure Pinbacker can speak for himself as to his intent.

It's true there is no "Academy" that dictates English usage to the masses. It's more a democratic thing, than a dictatorial thing. Much as Wendy would love to be on the dictatorial committee, that's just not part of our culture.

But there is a current consensus as to what English words mean and how English speakers use them. Dictionary writers are in the business of documenting, in a fairly scientific way, what that usage actually is. They are not, these days, generally in the business of advocating what they personally think it should be. At least, not in a dictionary.

All I want to advise Pinbacker is that Wendy has taken the stance that she disdains the consensus and has coined terminology of her own, as well as her own meanings and usages of common words, contrary to the consensus. She demonstrates right in this thread that it's an agenda with her. So she simply is not a reliable source if you want consensus definitions.
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Kodegadulo
Posted: Apr 4 2016, 12:41 PM


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QUOTE (wendy.krieger @ Apr 4 2016, 11:56 AM)
ut Kode does not like that terminology, so we're not allowed to discuss it.

It's true I despise your coinages. But I've never said that we should never discuss your ideas. I've only questioned why we are forced to discuss your ideas in every thread in this forum. You have now carried on this latest diatribe against me across no less than three different threads, in different subforums. I'm sure the original posters find much of this intrusion unwelcome. You have an entire subforum devoted entirely to topics of your choice. But I notice that when you post threads there, they don't get a lot of comment. Gee, I wonder why that could be? Could it be that people aren't that interested in all the stuff you happen to be preoccupied with? Perish the thought. You can't accept that, so you have to impose yourself on everyone.

Just as you have the right to post your ideas in your own threads, other people have the right to ignore you. That is all that I have been trying to tell Pinbacker here. Your opinions do not reflect the consensus, so he need not pay them any attention. Or he must take them with a big grain of salt. But you can't simply stand in the middle of the road like a spoiled child and demand attention.

I'm the focus of your ire, but it's not becayse i'm the only one here with this opinion of you. I just have the misforrtune to be the only one here who has no compunction about telling it to your face.
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wendy.krieger
Posted: Apr 4 2016, 01:05 PM


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The answer is perfectly simple, I imagine.

I put a legitimate answer discussing names that Pinbacker was asking, and said that the English use follows that of the decimal system. This leads to problems because a paradigm shift is needed to handle larger bases.

I get a response of "don't believe her, take everything with a grain of salt, she's into everything from HLU to polytopes" with the implication that the broad interests must be shallow and she is an idiot.

I maintain a dictionary on a scientific study. I know what the state of the 'established' terminology is, and the sorts of things you get people asking about. You get PhD students and graduates and professors coming and talking to me. I know what happens when words go from subject to subject.

You see, ordinary folk are asking scientists for precise words for precise things, and science does not work that way. They make a series of stepping stones using stretched imagery of words, and when they want the real word, they stick something else in.

People who play cellular games (like D&D and all those war-games), or cell phones, all assume a cell is a bubble in a foam. That is, regardless of the shape, the plane is covered with them. (Cell phones refer to the cells controlled by the towers at the centre. In Commonwealth english, we call them mobile phones).

So people make a Schleigel diagram of something like a 120ch, and it looks like a foam of cells, so we end up with a cell as a 3d element of a 4d thing. And then Coxeter uses it as a (n-1) element of an n-dimensional thing.

I asked Norman Johnson what he was going to do with cells in 'cellular automata'. A new word 'cellule' for what everyone else calls a cell. But if you ask him what a cell is, it's actually what we call in the PG, a 'choron' <- gk camera. Of course, mangled by Johnson for Bower's benefit. Cellule has made it to the wikipedia, in the names of some figures.

What I'm saying is that if you follow decimal-like terminology, you think of all bases as a kind of 10, and try to solve the problems of making 1,0 digits (eg icarus), and simplifying the 1,0,0 tables.

Twelfty breaks the simple decimal 'digit' into three or four distinct things, which have different implementations. This is not a bad thing, because when you look at the sumerian numbers, they separate things are already there, but we bundle them beforehand.
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Kodegadulo
Posted: Apr 4 2016, 01:31 PM


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Trying to keep it relevant to this thread:

Everything you claim about your terminology for large bases can be covered entirely by applying the concept of recursion to the concept of bases and their "digits". Encoding a "superbase" in a smaller "subbase", in order to simplify the problem of representing the values, and doing computations on them, does not require any new concepts, other than the process of recursion or nesting.

The only innovation you've suggested is the idea of alternating subbases. But even this can be subsumed into a theory of recursion: Simply note that some superbases can be decomposed into sets of alternating subbases. Even the notion of different "carries" across different "columns" is covered by this. I was easily able to adapt my base annotation scheme to accommodate multiple subbases, and that dovetailed with what other folks here were groping for. And Treisaran came up with a clever adaptation of SDN terminology to enable people to easily provide names for any alternating superbase, even sensitive to order of alternation. This is what it means to collaborate. But it doesn't fit your grandiose hopes for a "Wendese paradigm shift", or your stilted analogy of abacus rows and columns, so you are up in arms about it. Sorry to tell you, lady, but not too many people seem to be buying what you're peddling.
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wendy.krieger
Posted: Apr 5 2016, 12:52 AM


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The fact that all i see in SDN is duck-talk esperento does not mean that i'm running you down at every instance, telling people on every thread that you're strange and your agenda is to smother anyone's efforts in a layer of SDN.

Even though I appreciate that you are not fond of me using words from my sources, and so forth, and that i dabble in other arts too, you really don't have to go around and tell people to avoid me. Most people are perfectly capable of making their mind up.

The alternating base paradigm really is an advance. It does not look like one, but we have people talking in staff and twistaffs, means that the word 'digit' maps onto three different concepts, and that these need to be respected. Also, alternating arithmetic is assymetric, where as all of the attempts here have been symmetric.

Sometimes the best things are simple. Just not obvious.
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Kodegadulo
Posted: Apr 5 2016, 01:30 AM


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QUOTE (wendy.krieger @ r 5 2016, 12:52 AM)
The fact that all i see in SDN is duck-talk esperento does not mean that i'm running you down at every instance, telling people on every thread that you're strange and your agenda is to smother anyone's efforts in a layer of SDN.

Boo hoo, poor little Wendy. On the contrary, you have quite a bit to answer for in that regard. The insults, the put downs. The unnecessary attacks on my country. Your arrogant jingoism. Your lies about what is and is not English. You cannot even see the ironic hypocrisy in this very paragraph of yours. Or you think the people on this board are too stupid to recognize it.

I do not smother other people's efforts in SDN. Or Quantitels. Or base annotations. They find these to be useful tools that enable their own efforts. And people choose to use them, because they simply make sense. But if someone like gingerbill wants to go a different route with IDUS, it's no big deal. But you leap onto every thread here and it's wall-to-wall twelfty, and primes, and google-numbers, and polytopes, when most here have no interest at all in large bases, or prime hunting, or cryptic bit-packing, or multi-dimensional geometry. You habitually drive threads wildly off-topic--I mean, just look at this thread! What did Pinbacker want to do with all of this?

The best things are simple. But you have no idea how to get to simple.

But you know, I look forward to hearing about another case of a best practice that you disdain, so I can go learn about it and add it to my repertoire.
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wendy.krieger
Posted: Apr 5 2016, 02:09 AM


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You should feel honoured.

In any case it went off-topic in the post that directly followed mine. You felt a need to advise against me, and i notice earlier in the the thread there are cute parodies of me (including one that hasn't mastered upper-case and lower case thorn).

What I said in my post is concensus stuff, and where it deviates with it, it is stated how and why.

Kode decides to drag the topic offline, and blame me for it. He was already making noises about it before I joined.
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wendy.krieger
Posted: Apr 5 2016, 03:14 AM


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Pinbacker's question was to fill in 11 or 12 expressions which he designated XXX.

Glyph is, as i agree with icarus, a Mayan rune. Faces carved on stone.

Character is a word that refers to anything from Donald Duck to the idylic nature of the english countryside, to any sort of personal trait, to any rune set in text. It's overused.

Symbol is anything that one associates with: this flag is the symbol of our power.

Rune means 'secret', Runnemede (Where the Magna Carta was signed), is a secret garden. I use rune to specifcially point to a symbol of writing.

A numeral specifically refers to the runes that occupy places of number.

A digit refers mainly to the place, and then to what occupies it. A calculator having 12 places still is a decimal calculator. It just takes twelve-digit words.

Reference to Science

Science takes the above, and applies it to 8 and 12 and 16, and by golly it works, so let's use it everywhere!

So if it works with these bases it must make sense at base 60 or 7183 too. If you get over the tables problem, you really can use your four-function calculator as the sum and times tables in base 7776 or 5832.

But the terminology is not much help finding the solution for the times tables in base 60, and the imagery is wrong when applied to sumerian numbers.

Reference to twelfty

The key to breaking the tables problem is to break the base down into a smaller base, and use a series of carries. This break the decimal digit into three or so different meanings, and the word digit can't be directly into a word, just like early does not always translate to precocures (or whatever).

Moreover, written numerals do not make a complete apprasial of numeric systems. French "deux mille trois" means 2003, but is not a direct transliteration of it. The zeros are not said. It is more akin to 2 M 3, rather than a place-scheme.

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Kodegadulo
Posted: Apr 5 2016, 03:27 AM


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You know, Pinbacker, there is actually a very, very simple solution to the difficulties and complexities presented by large bases. As well as the problem of deciphering Wendy's garbled English, and her garbled logic.

Don't bother. Don't worry about it. You're not missing much.

Most of us here are here because of dozenal. We think it's a pretty good base. Versatile and human sized.
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Pinbacker
Posted: Apr 5 2016, 03:39 PM


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One last test:

user posted image

I highlighted three things in red, green and blue on the previous image.

Replace if possible the XXX placeholders by either the word "numeral(s)" or the word "digit(s)". If none of these two words fit perfectly, find another word that fits better.

Red and green are the same XXX. Red and green are different XXX.

Blue and green are the same XXX. Blue and green are different XXX.
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Kodegadulo
Posted: Apr 5 2016, 04:10 PM


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Red, green, and blue are all symbols, characters, numerals, and digits, depending on how specific you want to be. Digit is the most specific category they belong to.

Red and green are two different characters (or digits or numerals or symbols), from two different languages, representing the same digit value. They are different in shape, pronunciation, and language. But they have the same numeric value. They represent the same number.

Green and blue belong to the same language, but they have different numeric values. They are different in every other respect: different digits, different numerals, different characters, different symbols, different shapes, different pronunciations, different names. They represent different numbers.
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Pinbacker
Posted: Apr 6 2016, 02:43 PM


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What I am looking for is a simple word with the following definition.

A XXX is an integer between 0 and base-1.

In the image that I previously gave:
Blue and green are two different XXXs.
Red and green are the same XXX.

Each base/radix has precisely base XXXs. (Here by "base" I'm referring to the quantity of XXXs in the base.)

XXXs depend on the base/radix. Base 2, base 10, base 12, base 16, base 18, all have a different set of XXXs.

XXX do not depend on the specific numeral system, as long as the base/radix is the same for each numeral system. So all the following numeral systems that are base 10 have the same set of 10 XXXs: Western Arabic, Eastern Arabic, Devanagari, Gujarati, Gurmukhi, Limbu, Bengali, Oriya, Tellugu, Kannada, Malayalam, Tamil, Tibetan, Burmese, Thai, Khmer, Lao. (These are all the numeral systems in the previous image.)
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Kodegadulo
Posted: Apr 6 2016, 02:57 PM


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It's all a matter of context. On the one hand "digit" has a simple mathematical meaning which is the one you are looking for, as long as we ignore language and typographical differences:

A digit is an integer between 0 and base-1.
Blue and green are two different digits.
Red and green are the same digit (in different languages).

And so forth, substituting "digit" for XXX everywhere.

In the context of linguistics and typography these are all different character codes with different images and names, but that's a different world. If it becomes necessary to deal with both worlds at once, then we start having to clarify the difference between a "digit character" (the linguistic thing) versus its "digit value" (it's mathematical meaning).
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wendy.krieger
Posted: Apr 7 2016, 07:33 AM


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Red and green are the same numeral in different scripts, rather like five and cinq.

Green and Blue are different numerals in the same script, rather like cinq and huit.

Basically, script here is that things like Russian and Ukraine are written in the Cyrillic script, while French and English are written in the Latin script. Arabic uses a different script, as does chinese.

When you look at the scripts, they could be alphabetic, or they could be syllabic (like Korean), or ideographic (like chinese). But they're all scripts.

Scripts are comprised of glyphs, and one then decodes these glyphs into something else.
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Kodegadulo
Posted: Apr 7 2016, 10:18 AM


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QUOTE (wendy.krieger @ Apr 7 2016, 07:33 AM)
Red and green are the same numeral in different scripts, rather like five and cinq. 

Green and Blue are different numerals in the same script, rather like cinq and huit.

Yes, those are correct statements, but they do not contradict what I said before. All of these are numerals. They fall into the general category of being numerals. And they do belong to various scripts. But more specifically, they are digits, which is a subset of numerals. And the scripts belong to various languages.

We call these numerals digits because they are used in positional place value representations of numbers. There are other characters in Unicode which might be numerals but not necessarily digits.
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