Peano Postulates

[xilman]

Originally Posted by garo

@Wacky: It doesn't really matter. You can use both notations. IV is marginally more compact but ancient romans used IIII as well.

@xilman: Thanks for your exposition on multiplication. BTW, it's Arabic (really Indian) and not (really Hindu). There were probably some Budhhists and Jains in the mix as well :)

In my view it does matter. (And you are choosing an unintended meaning of "Hindu" from several in the English languge. Apologies for the ambiguity, but as we were discussing an archaic notation, I used the archaic meaning of that word, not least because it's the adjective which seems to be most frequently applied to our present notation.)

As noted, using the subtractive notation makes arithmetic more difficult. It is also a recent invention. There are many other such recent inventions in Roman numerals --- how many people here know that E is the Roman numeral with the value 250 for instance?

I suspect that the reason why we now use only the classical Roman notation, with the addition of subtractive forms, is that we only ever see them on clock faces and in simple lists such as page numbers. On clocks especially, the space saving of IX compared with VIIII is quite significant.

Sometime I may expand on the relationship between Western tally counting and Roman numerals, but that's for another posting.


Paul

[garo]

Originally Posted by xilman

(And you are choosing an unintended meaning of "Hindu" from several in the English languge. Apologies for the ambiguity, but as we were discussing an archaic notation, I used the archaic meaning of that word, not least because it's the adjective which seems to be most frequently applied to our present notation.)

OKay this is slightly OT but to use the word "Hindu" to describe things from the Indian subcontinent died with the Raj. It is archaic usage and may be considered offensive by some.

And the Mathematics history archive at St. Andrews uses the term Indian numerals http://www-gap.dcs.st-and.ac.uk/%7Eh..._numerals.html

[xilman]

Originally Posted by garo

to use the word "Hindu" to describe things from the Indian subcontinent died with the Raj. It is archaic usage

That's exactly what I wrote! An archaic usage chosen because we were discussing an archaic number system.

The etymology is straightforward. Many people who live in what you and I call "India" call their country "Hind", and so Hindu means (in admittedly archaic usage) "pertaining to Hind", as "Hindi" refers to a language natively spoken by many people who live in or whose recent ancestors lived in Hind.


Paul

[garo]

Umm, the term Hindu is not used for the inhabitants now and was never used by the inhabitants for themselves at any point in time. It was only used by the British. Hind is indeed the Urdu word referring to the country. But in Urdu, an inhabitant of the country is called a Hindustani and not Hindu. Hindu is used exclusively for the adherent of a religion now. I agree that the etymology is simple and that the word Hindu originates from Hind but the fact remains that the word Hindoo (or Hindu) is not considered polite when referring to the inhabitants of the country. But I also concede the point that you were knowingly employing archaic usage given the subject under discussion.

Anyway, this is going quite off-topic and reminds me of the big row on Wikipedia over naming the article the First Freedom Struggle or the 1857 Mutiny or the 1857 war etc. etc.

[xilman]

Originally Posted by garo

But I also concede the point that you were knowingly employing archaic usage given the subject under discussion.

Anyway, this is going quite off-topic and reminds me of the big row on Wikipedia over naming the article the First Freedom Struggle or the 1857 Mutiny or the 1857 war etc. etc.

There is another big dispute about the etymology of the term "Hindu Kush", which is a mountainous region in the north of the Indian subcontinent. "Kush", or similar words, means "slaughter" in some languages of the region. The dispute is whether the Kush in question is derived from those languages and, if so, whether it refers to or adherents to the Hindu religion, non-Moslem people, or to Indians generally irrespective of religious affiliation. There are several other possiblities for the etymology for "Kush", some of which are well-attested back to at least the late seventeenth century.

I'm also reminded of the politics concerning the terms "England" and "English". Many Americans use them when the politically correct terms are "United Kingdom" and "British" respectively. Although English myself, and so don't feel the same angst as some Scots, Welsh, Irish, etc, I do make a point of distinguishing between the English language and the American language, purely to irritate the colonials in return. Of course, the Canadians then get upset because although they are American, they are not citizens of the USA. Oh well, can't please them all.

I agree, this is now seriously off-topic.

Paul

[ET_]

Originally Posted by xilman

I'm also reminded of the politics concerning the terms "England" and "English". Many Americans use them when the politically correct terms are "United Kingdom" and "British" respectively. Although English myself, and so don't feel the same angst as some Scots, Welsh, Irish, etc, I do make a point of distinguishing between the English language and the American language, purely to irritate the colonials in return. Of course, the Canadians then get upset because although they are American, they are not citizens of the USA. Oh well, can't please them all.

Sounds like Winston Churchill's quote about his "twin nation"...

Something like "They are not different from us... apart from language"

Luigi

[cheesehead]

I advise any USAers going to the UK for the first time (as I did in 1983) to try to find an "English-American/American-English" translation dictionary before their departure (if possible) or in the first tourist shop they find after arrival. Hmmm ... that may be available on the Web nowadays.

[mfgoode]

Lets get back on topic.
I was simply amazed at the overwhelming response after my controversial remark I made to Cheese head for which my apologies.
Thank you Garo, Xilman, Wacky and Cheesehead (in order of posting).
Firstly I am sorry Cheesehead if my remark was in any way offensive to you. Really there is no difference in our opinions and we still see eye to eye.
On the brighter side it was an effective catalyst to generate a spirited reaction from the others and I m very grateful at the wealth of information in this thread.

Garo: Thank you for your lucid explanation and to have set the ball rolling.

Xilman: I know that with your study of ancient hieroglyphs this was a piece of cake for you. Explaining multiplication in Roman Numerals (RN) is commendable.
“I fully concede that division of RN is rather difficult”
It is up to us to crack this code.

Wacky: “However in the compact notation you must give a coefficient of -1 to any symbol that occurs ‘out of order’ ”
This is an astute observation in deed.

If old Georges Ifrah consulted you three before writing his 3 volume work I think he would jolly well stop harping through out Vol.1 that RN and other ancient systems were “unusable, and downright obsolete in concept”

Ifrah does say however “to multiply or to divide it was in fact enough to know how to multiply or divide by 2 ”
I’m sure Paul you can work further on this lead.

Cheese head: You drew on the idea that for centuries man did without the decimal system we have today and that the ancients got on well despite not knowing it .This is very true indeed.

Xilman: Regards RN and clock faces you are right but you will be at home in Italy esp. Rome as the dates on ancient buildings are all in RN.
“ Sometime, I may expand on the relationship between Western Tally counting and RN”. Now is the time to do it and it’s never too late.

Garo: The website you gave was really excellent and I also read thru the links the whole of last evening but I have still got to do a second reading.
It spurred me onto reading my own books on Vedic maths and Ancient Indian Maths which are being introduced in most Indian schools today.
I have often heard and read that the Sanskrit language is best for computers and so are the algorithms given in Vedic Maths.
Is there any truth in this?

Mally

[mfgoode]

Can anyone kindly explain to me how do we arrive at 0^0 =0 ?
when a^0 always = 1 Surely by continuity it should also be eqaul to 1 when a = 0?
2) By convention 0! =1 and 1! is also equal to 1. so 0 = 1 A paradox!
Mally

[R.D. Silverman]

Originally Posted by mfgoode

Can anyone kindly explain to me how do we arrive at 0^0 =0 ?
when a^0 always = 1 Surely by continuity it should also be eqaul to 1 when a = 0?
2) By convention 0! =1 and 1! is also equal to 1. so 0 = 1 A paradox!
Mally

Where did you hear that 0^0 = 0???

It makes sense, in many situations, to *define* 0^0 = 1, but it is
generally left undefined. I have never seen 0^0 = 0.

[xilman]

Originally Posted by R.D. Silverman

Where did you hear that 0^0 = 0???

It makes sense, in many situations, to *define* 0^0 = 1, but it is
generally left undefined. I have never seen 0^0 = 0.

Possibly from 0^x = 0 for all x>0.

Paul