nd-notation. How to count anything in tp?

[Baerdric]

Reply to Baerdric:

That's 211 fish, nanpa mute wan wan tu wan tu kala.

211 fish -- "kala pi nanpa tu nanpa wan nanpa wan"

That requires converting to base 10. Which brings in the missing 7 numeral names and several missing place column names. toki pona actually already has a ternary counting system, we just haven't adopted a positional notation yet.

[janKipo]

Right, which goes against the tresimal system.

[janpona120]

toki pona actually already has a ternary counting system, we just haven't adopted a positional notation yet.

Guess, the ternary counting system also is a positional one.

Can the ternary system solve mathematical tasks?

[Baerdric]

Well, "ternary" does mean base three, and base three is often used with a positional notation, but I don't know that it's required. Perhaps that's why jan kipo uses the term "triseimal", which, by context, I believe he means three digits (0,1,2) rather than base three.

And yes, any (Rational number) base numbering system can do the same math as binary or decimal. Base three has the interesting properties that 1/3 is a nonrepeating decimal number (0.1) whereas 1/2 is not (0.11111...)
https://en.wikipedia.org/wiki/Ternary_numeral_system

But otherwise you can build a multiplication tables and do all common math as directly as with any other positional notation except in this case (below) you would start from the left.

nanpa mute ala tu (=6)
en
nanpa mute ala wan tu (carry the wan) (=21)
li
nanpa mute ala ala ala wan (=27)
(remember it's reversed)
02+
012=
0001

To multiply I would probably overload the operator "mute",
nanpa mute tu
mute
nanpa mute tu
li
nanpa mute wan wan.

[janKipo]

Actually, "tresimal" was meant to embrace both three digits and positional notation with powers of three (but, admittedly, decreasing from the left). The first feature was imposed by the basic tp vocabulary, the second by the need to cover all the cardinal numbers (we have not got to considering fractions or decimal expansions, nor, of course, any operations).

[janpona120]

To multiply I would probably overload the operator "mute"

I have an idea to use for "multiply"-operation a tp-word: "sama" or "sin"

[Baerdric]

I was tempted to use sama as = (equals) but went with li. I still vacillate on that.
Obviously ante is subtraction, and while I had used en for addition, a verb like sin makes more sense.

Mute means multiple, I don't see sama or sin being an improvement over that but I'm willing to be convinced. And kipisi seems like a shoe-in for division although I understand it was not originally a word.

To me the main question about math is whether we need to mark the words for mathematical use.
"tu nanpa kipisi tu li wan"?

or just count on context, using the divisor (in this case) to modify the verb.
tu kipisi tu sama wan

pi might mark the decimal point to mean "and has the parts of".
nanpa mute wan (1) (nanpa mute now assumed for the whole equation)
kipisi ala ala wan (9)
sama ala pi ala wan (0.01)

nanpa mute tu ala ala wan pi ala wan tu (this would be base three 1002.012 in standard notation)
(in the case of decimal numbers, reverse notation already exists, so reversing it makes it look the same above, but I think it should come at the large end of the nanpa mute.
Again, the point is to avoid having to make up words for place values like hundreds or hundredths)
"two 1s, no 3s, no 9s, one 27 and has the parts of no 3rds, one 9th and two 27ths."

[janKipo]

As a survey question, I think that 'en' and then 'sin' have been most used for /+/. 'tenpo' and then (rather far down in popularity) 'mute' for multiplication (we skip over the devices used for the pu standard numeration). 'mute' fares better for exponentiation, insofar as anyone has gotten to that. 'weka' and 'lili' seem favored for subtraction, 'kipisi' for division (again, a rarity). As expected, 'pi' wins for the decimal place. The equation sign is usually just 'li' in the sentential form, though 'li sama' is used by some fuss-budgets.
In fact, these have not been common topics, since we do not have a number system to use any of them with any degree of seriousness.

[Baerdric]

Ugh! tenpo would be at best a pun for the englishification of multiplication!

OK, now that I've calmed down, maybe multiple tenpo (occurances) of adding the number...

My use of nanpa mute implies mute could be used in exponentiation. But then exponentiation is a form of multiplication. I think exponents are more like self multiplying (sama mute?) place columns are more like base value multiplying (nanpa mute), which leaves simple multiplying as simply mute.

[janKipo]

Well, of course, multiplication is just adding, so we are back to 'sin' which is ultimately just increasing by one. And so on. Profound mathematics doesn't play any role here; we just need words and any analogy will do (though I admit that calques are not something I like much).