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?
