Mathematics in toki pona

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Lingva lernado: Kiel paroli Tokiponon, tradukproblemoj, konsiloj, memoraj helpiloj, iloj kaj metodoj por pli rapide lerni Tokiponon kaj aliajn lingvojn
fouche
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Joined: Sun Sep 15, 2019 8:01 am

Mathematics in toki pona

Postby fouche » Sun Sep 15, 2019 9:37 am

Hello everybody!

What is the state of the art in mathematical definitions in toki pona?

Just for fun, I tried to define a few notions form basic set theory, logic, general topology and category theory (the mathematics I do for a living :) )

Sorted alphabetically, for ease of consultation:
adjunction : sama pakala
axiom : oko wile
category theory : kulupu sona
closed : selo
codomain : noka
commutative (diagram) : pona (sitelen)
complement (of a set) : mute ante ijo
conjecture : oko pimeja
corollary : oko tan
counterexample : ala oko
definition : oko ni
diagram : sitelen
domain : pana
empty (set) : ala (ijo)
example : oko wan
exercise : luka oko
finite (set) : lili ale (ijo)
forgetful functor : pakala suli tawa
free functor : sin suli tawa
function : ante
functor : suli tawa
group : kulupu (ijo)[1]
infinity : ale
intersection (of sets) : mute pi tu ijo
inverse : ante
isomorphic : tu sama
isomorphism : tawa sama
kernel : insa
lemma : oko lili
logic : sona wile
mathematics : sona kon wile
monoid : kulupu ijo ala ante
morphism : tawa
natural transformation : pona tawa
object : ijo
open : ala selo
opposite category : ante kulupu
philosophy : sona kon
physics : sona kiwen [2]
power set of uncountable : suli suli ale[3]
ring : tu pona kulupu
semigroup : kulupu (ijo) ala wan
set : mute or ijo
theorem : oko kin
uncountable infinite : suli ale
union (of sets) : mute tan tu ijo

==

[1] The notion of group is central: whatever adds structure is a kulupu ijo, an "organized collection", with some more property; whatever subtracts structure is a kulupu ijo without something.
[2] chemistry, geology, astronomy: it's all sona kiwen.
[3] in general, (suli)^n ale = 2^(2^ (... 2^omega)); note that this means that in toki pona the generalized continuum hypothesis holds.


Arts and sciences are all sonas:

sona kiwen : physics
sona kon : philosophy
sona kon wile : mathematics
sona wile : logic


All classes of mathematical statements have to do with "vision", so

oko wile : axiom (see what I want)
oko kin : theorem (see to confirm)
oko lili : lemma (see a small [tool])
oko ni : definition (see that)
oko pimeja : conjecture (see in the dark)
oko tan : corollary (see because of [something prior])
oko wan : example (see one [instance])


Comments are more than welcome, especially to expand this stub of a dictionary. Even more so, because I'm sure most of these translation can be improved/simplified; also, I'm not claiming originality: there must have been somebody who already did this :)


PS: What if I wanted to write a small dictionary in LaTeX, and a brief composition in tp, using a dedicated script? Is this an acceptable choice, and if yes, how is it used? It seems to be that here only some digraphs are present; what are the precise rules for their construction? What about more complex stacking of symbols, like in sitelen sitelen?

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jan_Lope
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Re: Mathematics in toki pona

Postby jan_Lope » Mon Sep 16, 2019 8:40 am

fouche wrote:Hello everybody!

What is the state of the art in mathematical definitions in toki pona?


toki!

It is not the goal of Toki Pona to be able to represent mathematical connections.

Please see
https://htmlpreview.github.io/?https:// ... 0000000000
pona!
jan Lope
https://jan-lope.github.io
(Lessons and the Toki Pona Parser - A tool for spelling, grammar check and ambiguity check of Toki Pona)

On my foe list are the sockpuppets janKipo and janSilipu because of permanent spamming.

fouche
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Joined: Sun Sep 15, 2019 8:01 am

Re: Mathematics in toki pona

Postby fouche » Tue Sep 17, 2019 9:59 am

Mathematics is about structure and isomorphism, not about numbers. sona kiwen is about numbers.

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jan_Lope
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Re: Mathematics in toki pona

Postby jan_Lope » Wed Sep 18, 2019 12:56 am

fouche wrote:Mathematics is about structure and isomorphism, not about numbers. sona kiwen is about numbers.


toki!

I might. But Toki Pona cannot describe complex structures or complex isomorphism either.
pona!
jan Lope
https://jan-lope.github.io
(Lessons and the Toki Pona Parser - A tool for spelling, grammar check and ambiguity check of Toki Pona)

On my foe list are the sockpuppets janKipo and janSilipu because of permanent spamming.


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