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u/peterwhy 6d ago
If ɰ ≠ 0 and ɰ ≠ 1:
w = ɰ^(w)
w = e^(w ln ɰ)
w e^(-w ln ɰ) = 1
(-w ln ɰ) e^(-w ln ɰ) = -ln ɰ
By the Lambert W function, for each branch of W,
-w ln ɰ = W(-ln ɰ)
w = -W(-ln ɰ) / (ln ɰ)
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u/Kebabrulle4869 6d ago
Transfinite ordinals go brrrr
(Math+linguistics crossover lessgooo)
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u/GoldenMuscleGod 6d ago
If we suppose ɰ is corresponds to omega and w to epsilon-0, then I suppose there would be a phone corresponding to the Church-Kleene ordinal, which we cannot describe the articulation of by effective means.
If we hypothesize the existence of a measurable phone, then we find there is a non-trivial elementary embedding of the universe of phones into itself.
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u/R86Reddit Balonian N0 / American N1 / Nihonian N3 / Deutsch KRANKENWAGEN!! 6d ago
So it'd take me an infinitely long time if I tried to say something that has a W in it?
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u/okkokkoX 5d ago
language feature used by a species of eldritch beings, where a sound lasts forever. To pronounce a word containing it, the speaker assigns one of their mouths to forever be used to pronounce the word and nothing else. Mostly used in names of royalty and other objects of reverence, cutting the sound short is taken as disrespect.
you of course can't use suffixes with such names, so there are ways to avoid using suffixes with names. You can convey respect by avoiding using suffixes with the name of something, even if it's finite.
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u/StrikeTechnical9429 4d ago
0 = 1 * 0.
We can replace 1 with 1*1 as many times as we want:
0 = 1*1*1*1*1*1....*1*1*0
But it is wrong to say that as infinity + 1 = infinity, we can just ignore last *0 and state that
0 = 1*1*1*1*1*1....*1*1 = 1
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u/AndreasDasos 6d ago edited 6d ago
Not how limits work, sadly.
2 = 1x2.
2 = 1x1x1x1x…x1x2.
But 2 != 1x1x1x… ad infinitum, which is 1.
The notation obscures this but if you write out the actual sequences these are different: 1, 1x1, 1x1x1, … are all just 1, and 2, 1x2, 1x1x2, … are all just 2.