/sci/ - Science & Math

>>16207285
Mostly not meaningful. If we take “finite set” to mean it has a bijection with {0,1,..,n} for some n, then “countably finite” is redundant, as you pointed out.

In advanced mathematics, especially mathematical logic, they do play around with the meanings of words, and then you assign a meaning to “uncountably finite”. These always have something to do with the set being small, but also complex. The complexity makes it so that (in your weird chosen system) there is no function that would make it “countable”.

These things happen a lot in constructive/computable mathematics, and in versions of set theory where you drop the Axiom of Choice. But this is pretty niche stuff.

>>16207396

Now that I've heard someone put it like that, "uncountably finite" feels like a way to describe "God only knows" things like the number of grains of sand on a beach. One could hazard a reasonable enough guess, but getting a precise count would be nothing short of a miracle.

>>16207285
>Is uncountably finite in any meaningful way a thing
Count the exact numbers of molecules in your body. It's a finite number, after all. Only we can never count it, we can never have perfect enough information about our bodies and everything inside it to be able to do that, and the number changes every time we breathe anyway.

>>16207499
>too many possibilities for our tools
>>16207504
>information keeps changing
Yeah, it’s usually something like that. But these are niche settings where definitions and axioms have been altered. Of course finite sets are countable when you are not in one of these niches.

>>16207285
>Is uncountably finite in any meaningful way a thing, or would that be inherently contradictory?
Like counting all numbers between 1 and 2, for example?
In practical physical terms, no, due to the Planck limit, assuming we got quantum physics right.

>>16207396
I choose not to laugh with you for it may affect my mortality.

ok a set that is bounded but cannot be counted
If I covered a glass with a cloth and broke it under the cloth the number of broken pieces is finite but indeterminable.
In math we say something is countable when we relate it to the natural numbers so I don't know how it's possible but that would be my general intuition about the idea.
Maybe this proves set theory is inadequate.

>>16207499
You're retarded. Something being "hard" to count is not objective. Grains of sand are the beach are certainly countable. There is a finite number of them.

>>16207615
Retard.

>>16207617

>>16207615
Ok I did it. I call it a gassy set.
It's like a jar with a hole in it. The space is finite but because air is compressible we don't know the exact number of particles
here is a simple gassy set I thought about
it has a set oscillator that oscillates between the empty set and a singleton. You might say it's dependent on an independent variable but it's not because we don't need any initial conditions to define it.
This set is uncountable because {0,1} is not an element of the naturals (including zero).
I actually think gassy sets are pretty cool. I think they could also be called oscillator sets but gassy sets sounds funnier.
Not that you can have element wise permutations but if you still have the same count regardless you still have a countable set, so that's how I knew I had to break the whole idea by making the count result in another set instead of the set being a subset of the naturals. So it's interesting though because the resulting set was countable. I wonder if it's possible to have a special set that always returns a gassy set. It's stumper to me and I'm tired anyways. I just like fucking with set theory since I fucking hate the field so much. I can only hope this result in the suicides of some ZFC trannies.

>>16207622
Meds. Now. Then promptly kill yourself.

>>16207632
just like the old days
don't worry I won't have any schizophrenic episodes this time, it was just a silly idea. I'm retired from math anyways. It's not healthy for me. Ever since I cured my own schizophrenia I told myself to avoid math. I don't need any meds though I did it the old fashion way.

>>16207622
>he thinks that creating different rules for a given set type invalidates set theory
>when https://en.wikipedia.org/wiki/Multiset#Generalizations is
God what a retarded meta-nigger you are, glad you cured your schizo-ism or something, have good life and all that

>>16207285
The problem is that you let someone convince you that infinity is a legitimate concept and pure math is meaningful in any way.

>>16207285
The concept of countability is fundamentally flawed and I have proof. No I will not show you... yet.

>>16207617
But like...erosion.
It makes the sand smaller every second.
And at some point, sand stops being sand and becomes part of water turbidity.
How do people like you exist? I guess you are just young.

>>16208574
Multiplicity sets?
Is this what cope theorists are up to these days?
They have nothing on gassy sets.

>>16208616
It is a valid concept it just means no end, you just interpret it in retarded ways to someone how mean that there is an end that is really really far away when that is not what the concept means at all, infinity is not an actual number, it just describes the lack of upper limits to the numerical system.

>>16211121
>it just means no end
>infinity is not an actual number
And yet people make equations with infinity in them.

>>16211410
>And yet people make equations with infinity in them.
As a limit.
>but
Transfinite ordinals are limits and transfinite cardinals are defined in relation to transfinite ordinals. You literally cannot get to infinity in a mathematical formula without implicitly or explicitly taking a limit.