Infinitism Vs Finitism

[keen marlin]

I actually think you can variably prove infinity to be present within this world using cantor's diagonal argument, which would entail aleph 1 being real, logically making aleph null (baseline infinity) real (or possible)
I'd like to hear other peoples perspectives/ reasoning for whatever side they choose

[burnt otter]

How exactly is that proven? In any case, the proof must be somehow invalid. Because it appears all our observations are equally well-explained by a universe with discrete finite spacetime.

[deft quest]

How in the hell do you plan to apply Cantor's diagonalization argument to... what, space?

[burnt otter]

Yeah. And your argument that the existence of ℵ₁ implies the existence of ℵ₀ is unjustified. Not to mention that the diagonalization argument itself assumes the existence of infinite strings of digits. Please elaborate.

[urban perch]

thats not forbidden

[urban perch]

that is some pseudo philosophical mumbo jumbo

work with whatever formal system you want

neither infinitism nor finitism is 'better' than the other

[somber shell]

At least your're thinking differently

I like that

[ruby cairn]

I think it has to do with interpretation

I think you can encode infinitism in finitism

[urban perch]

inuitionism doesn't permit nonconstructive arguments

at the very least, the "encoding" will be difficult

[ruby cairn]

What's finitism and infinitism actually?

[urban perch]

broadly speaking, finitism = "only finite objects exist"

for intuitionists infinite objects like infinite sets don't (and can't) exist

the word "exists" is also another can of worms, entirely

their definition of N (the naturals) has something to do with memory capacity of computing devices

it's not a completely unreasonable position to take - computers don't "understand" and can't model the concept of "infinity"

any computer is bounded by 2^N bits of data, presumably there being some theoretical upper limit to maximum memory capacity

none of this is rigorous, take it as a tongue-in-cheek

rigorously speaking however: given sufficiently sophisticated formal system (one that encodes the arithmetic of N), the only way we have for determining whether it is "good" or "bad" is whether or not it produces contradictions

if we don't allow infinite objects, that's fine - but then that formal system wouldn't be useful for analysing infinite dimensional banach space theory

[valid hazel]

This is not something intuitionists generally believe.

[urban perch]

also possible

I've also heard a certain mathematician saying the largest natural number is one that will be referenced by humans

[valid hazel]

Yes, those are ultrafinitists.

[valid hazel]

This is not really the case. Finitists have robust, ontological disagreements with infinitists. It's similar to saying, in response to a dispute amongst neccesitarians and non-necessitarians, that it just depends on what modal system you adopt.

[urban perch]

disagreements naturally arise

mathematically speaking one should only worry about what the basic truths (axioms) are and what can be deduced from them

[valid hazel]

Yes, but you can dispute over the basic truths.

[urban perch]

for something like CS, I would actually prefer constructivist approaches

[valid hazel]

Yes, same here.

[urban perch]

indeed, but then that would be a philosophical debate

[valid hazel]

Indeed, but I don't really think there is nor ought to be a clear dermarcation between philosophy and all the other disciplines.

It's not as if our mathematical axioms (which tend to be formulated in natural language) and proofs which are accepted by other mathematicians just popped out of the ether.

[urban perch]

im a mathematician, i am by default equipped to sh.t on philosophy 😂

[valid hazel]

yeah, people tend to (mainly people who know nothing about it!)

though i wouldn't say you're equipped to

[urban perch]

😂

[valid hazel]

ig maybe you are

like, a large number of post-20th century philosophers who started the analytic tradition had firm mathematical background for a reason

it's hard to interface with a lot of analytic philosophy without a firm logic background

im also compelled to shit on philosophy, but i don't really share the same tendency to just outright dismiss entire fields of study like some people do

[urban perch]

difficult to put my position into words tbh

empirically speaking, such discussions (for me) have sooner or later come down to personal beliefs

i can't deny someone their belief

[valid hazel]

Ah, is the idea that certain disputes aren't empirically verifiable, and thus there is no real way to justify one view being correct over the other, or...?

[urban perch]

something like that

math is simple in this regard

the rules of the game are fixed

but I don't know what the whole rulebook of philosophy is

[valid hazel]

kind of, the rules of the game are less apparent than you'd think

i have a natural inclination towards the accounts of people like Reuben Hersh or Imre Lakatos

[urban perch]

hence I am content with all formal systems existing, their usefulness dependent on context

[valid hazel]

i mean, intuitionists don't tend to say "this formal system is haram" or something

it's much more like "in reality, PEM is false"

[urban perch]

my belief (yup, here we go 😄 ) is that usefulness of theory A or B is dependent on context

what sort of problems are we trying to analyse

[valid hazel]

You're going to have to elaborate. Almost nobody will reject the "usefulness of theory A or B is dependent on context" simpliciter.

[urban perch]

fair

[valid hazel]

That doesn't counteract any grand view though. Like, here's a good example of a view a lot of people who endorse classical logic hold: the very meaning of negation entails the PEM, so intuitionist logics negation means something different.

[urban perch]

for example, I would (in most cases I can think of) require axiom of choice for banach space theory

and a lot of theory I am familiar with is predicated on the Hahn Banach theorem

[valid hazel]

Yes, well, keep in mind, most people do not want to put a ban on working in systems that contain AC as a theorem.

Like, formal systems are kind of divorced from what people who have these disputes care about

This is coming from someone who doesn't really think there's a fact in the matter of whether AC or PEM is true

[urban perch]

PEM

excluded middle ?

[valid hazel]

Yes, PEM is LEM for people who don't want to call it a law, common sometimes among (certain) intuitionists

[urban perch]

understandable

side note: choice implies PEM

[valid hazel]

Yes

Which is why intuitionists have to reject it 😆

No, some philosophers (who are also mathematicians) of mathematics like to do a thing where they argue for some super intuitive thing Q, say it's true, and then show Q entails something like choice or the continuum hypothesis or something

What Woodin is doing comes to mind

However, this is all meaningless if you don't believe in what are frankly magic objects floating in the ether (mind-independent, aspatiotemporal "abstract objects")

I am reminded of how funny this is

[urban perch]

oh boy ..

I was in some argument with one N. Wildberger some years ago over some philosophical mumbo jumbo

[valid hazel]

Oh, how did that go?

You say "mumbo jumbo," so I assume you didn't know what the words he was using meant.

[urban perch]

he did enjoy sophistry, certainly

[valid hazel]

Exciting stuff, but this N J Wildberger fella I find online has a text literally titled "Divine Proportions"

Which is not a uh, good sign

[urban perch]

he had an annoying condescending tone

[valid hazel]

ah, yeah, well that sucks

[urban perch]

basically we were talkig about one of his essays where he criticised the ZFC axioms

I just should have known better that this premise alone is enough reason to avoid engaging with him altogether

[valid hazel]

eh, not all philosophers online are assholes (or sophists)

[urban perch]

but I was in my "I feel like a god" stage of my math education

feeling like I should "save everyone"

[valid hazel]

saving everyone is a very noble goal, even if it is ultimately very misguided

so, what happened?

[urban perch]

he talked in circles

I pointed that he is attacking his own strawman multiple times in the essay

essentially, he didn't criticise the axioms

[valid hazel]

damn, this guy seems somewhat respectable, teaching at UNSW

[urban perch]

but rather his understanding of the axioms

which is pointless, imo

yes, and also dabbles in some very non trivial math

has written papers on Lie theory to name some

[valid hazel]

yes, i am looking through his stuff on ResearchGate

[urban perch]

he also does youtube, and he has a series on history of math

which I enjoyed a lot

[valid hazel]

that's pretty good, he teaches history of mathematics at UNSW so it makes sense

[urban perch]

but then he's hellbent on redefining analysis

[valid hazel]

if you like history of mathematics, i recommend you check out joel david hamkins

[urban perch]

because the "real numbers" don't really make sense

[valid hazel]

ah, so it's some novel new type of analysis?

[urban perch]

recognise this name from overflow too

[valid hazel]

indeed!

I was going to say

just now

"you may have seen him on mse or math overflow"

[urban perch]

i think he does the same thing as analysis does now with limits

but he quantifies over Q

because that's somehow qualitatively different 😮

[valid hazel]

does he just dislike uncountability or something

[urban perch]

Q seems ok so he's not ultrafinitist

or maybe he is, I don't know to be fair

he has said something about there being the largest natural number

[valid hazel]

he probably dislikes R because equality is not computable or something

[urban perch]

something about it is unintuitive for him 😄

..pun intended

[valid hazel]

haha

[urban perch]

i dont rightly understand his position

Q seems fine for him

but he has also criticised the axiom of infinity

so he can't accept N (as an infinite set)

[valid hazel]

well, that's probably fine, it may be incoherent or something, but it also may be he didn't explain it well, or you don't have the philosophy background to make sense of his bad presentation or something, or a combination of the three

most likely a combination of the three

weird positions require a lot of deciphering to make sense of

[urban perch]

i'd assumed elementary logic would be enough

not PEM, but that's fine

[valid hazel]

eh, it probably is actually

sometimes there are weird philosophy-specific things, and if you touch enough logic, that's kind of inevitable since logic is basically at the junction between philosophy and mathematics, so the distinction gets fuzzy there

i'll try to read some of this guys stuff

[urban perch]

but whatever my disputes with him, he definitely knows math, it's not all bogus stuff on his channel

[valid hazel]

okay, from his overview of Divine Proportions, his concern is that a lot of contemporary geometry is hard for people to understand because of the semantic vagueities of "infinite set theory"

[urban perch]

oh yeah, he definitely doesn't like axioms

[valid hazel]

what he's doing doesn't actually seem all that bad, especially given how nice sufficiently weak systems are

i think his idea is actually just that we don't really have any understanding of this "infinitity stuff," so we should avoid it

which isn't all that bad, but i don't know what he uses to argue this is the case and what-not

[urban perch]

and if he did say it like that, that would be fine with me

but he gets veeeery condescending

[valid hazel]

ah, that's a real shame, seriously

[urban perch]

he claims that the ancient greeks and the reneissance folk were much more rigorous than we are today

[valid hazel]

haha, well it's hard for me to comment since i don't really know what he means by that, ancient greeks surely didn't prove theorems that turned out to be equivalent to AC in natural language, that's for sure

greeks didn't have any formal axioms or anything, obv

no formal proof checkers or anything either

[urban perch]

theory wasnt as developed in the early 19th cty so many mathematicians/physicists used some claims because they were intuitively correct

famous example: continuous functions are differentiable almost everywhere

[valid hazel]

yeah, it's just plausible the dude thinks this is still the case more than we let on

bc of the axioms he doesn't like or something

[urban perch]

and even more famous counterexample: weierstrass's continuous nowhere differentiable function

and even more, if what wildberger claimed was true

why oh why did hilbert go on to do what he did?

did the rigour of our ancestors got sucked into a black hole or something?

[valid hazel]

Are we talking about Hilbert's formalism stuff

[urban perch]

hilbert's programme i think it's called

[valid hazel]

Yeah, well sadly that failed

[urban perch]

but a good endeavor nonetheless

[valid hazel]

Indeed

[urban perch]

pushed people like turing and gödel

[valid hazel]

There are systems like relevant PA (PA closed under entailment in relevant logic) which have finitistic proofs of their consistency, which is neat

[urban perch]

good talk, gotta make dinner, tc buddy

[valid hazel]

alr, have fun and eat well

[keen marlin]

Dimensional space

[keen marlin]

Thanks

[keen marlin]

I totally acknowledge I could be wrong, which is why I said I think you could variably prove infinity to exist
Question to think about: How many squares are in a cube? (Hint: It's not 6)

If we break a cube down

There's an aleph 1 amount of squares

Another way to think about it: How do you go from a square to a cube with just squares? You need to somehow increase the third dimension from 0 to any positive number
How many numbers/decimals are there inbetween 0 and 1? Cantors diagonal argument pretty much self explanatorily applies to the amount of squares with no third dimension to make a third dimension

But other people could say something 2d doesn't exist and that it's an axiom
Which is again why I said variably since it depends how you look at it

[deft quest]

"Variable proof" is not proof.

[deft quest]

What are you even talking about?

[deft quest]

No, there isn't. A square is a shape with literally zero thickness, any "slice" off of a cube must have a nonzero thickness. You can take the limit as the thickness approaches zero, but that's not remotely the same thing. A limit approaching 0 is not a value that achieves 0. Also this has nothing to do with Cantor diagonalization, and also also this presumes the continuity of space, which is supposedly the thing being proved, which makes it circular.

[keen marlin]

I don't think you understand

[keen marlin]

I'm just not gonna respond I fear you've not grasped the concept

[deft quest]

I've grasped that you haven't taken calculus.

[keen marlin]

How old are you?

[keen marlin]

And I'm not old enough

[deft quest]

So if you think you have a revolutionary theory about some field of math or science, but you're too young to have learned the math that is literally freshman level in that field, what's more likely; that you've noticed something that everyone else has missed, I guess because they were too busy going to all those classes you haven't taken, or that you've missed something that everyone else has noticed, maybe in all those classes you haven't taken?

[keen marlin]

'the math that is literally freshman level in that field'. Calculus is part of set theory?
I quite literally said I acknowledge I could be wrong, and I wasn't expecting to run into passive aggresive adults on this app who have degrees in maths? I thought someone with such knowledge wouldn't be sat in discord servers but I guess I was wrong
And do you have selective reading? Why only respond to some of what I've said

From what I've gathered on google, set theory is the standard foundation

[deft quest]

..."freshman level" means "taught to college freshmen".

Something you learn in the first year of college.

[keen marlin]

So you're an adult?

https://tenor.com/view/get-to-the-point-hurry-up-golden-girls-speak-faster-whats-the-point-gif-21117514

Not too sure what you're clearing up

[deft quest]

And I'm not being passive aggressive, I'm making the point that you should take, like, literally any effort to seriously investigate an idea before you present it.

And if even that much feels over your head, you should acknowledge that you're probably just wrong.

[keen marlin]

Well yes you were
You started being passive aggressive before I even sent my theory
I find it sad that an adult is sat on discord to begin with, nevermind being passive aggressive to children and not even understanding what I've said

[deft quest]

What do you think "passive aggressive" means?

[keen marlin]

That's fine, and I even acknowledge it
You sure as hell haven't explained that

[keen marlin]

Let's use our common sense

And again

Let's circle back to the selective reading part

I'll ask again

How old are you?

[deft quest]

How can I "use common sense" to figure out what you think? Do you think "common sense" is the ability to read minds?

[keen marlin]

I fear common sense has the word common in it.. Common sense doesn't seem to be very common in you I guess?
Someone being passive aggressive means they're passively including unnecessarily remarks/ being aggressive in the way they talk
You could've deduced that if you'd utilised common sense
Definition is pretty much deduced within the phrase

Third time asking so hopefully will bypass your selective reading

How old are you?

[deft quest]

It's not "selective reading", it's ignoring pointless nonsense.

[keen marlin]

I would like to know the age of the person I'm engaging in conversation with thank you

You say calculus is something taken in first year of college, I'm asking how old you are to see if I can figure out if you've taken it or not, or how deep you are in mathematics

[deft quest]

I would like a billion dollars and a trip to the Moon.

[keen marlin]

I'm deducing from this you're either a child or an adult with a short temper

Based on your reply earlier, one with negligible comprehension skills and as established, no common sense

Nice chat

[deft quest]

This is literally the first thing I said. Do you think this was passive aggressive? Because it wasn't. It was confused. I was confused because the sequence of words you said made no sense.

[keen marlin]

I think it encompassed unnecessary remarks
What I said did make sense, just not to you
Which now makes sense since we've established you've got no common sense
You could've simply asked me to elaborate/explain
I read 'How in the hell do you plan to-' with multiple dots to be passive aggressive
Although that could've been deduced with critical thinking from my previous replies on the topic... (yes this is me starting to be passive aggressive)

You have time to type all this but not 2 numbers

Well I'm hoping for 2 numbers

[deft quest]

No, it didn't make sense because I knew what the words you said mean. Saying you can prove that infinity exists in reality using Cantor diagonalization is incoherent. I literally cannot think of an analogy for how little sense that makes that I'm confident you would be able to understand.

[deft quest]

...do you expect me to have two ages?

[keen marlin]

I don't think you understand what incoherent means

[keen marlin]

Oh honey...

[deft quest]

10^100. Now shut up about it.

[deft quest]

You also think you can apply Cantor diagonalization to space, so it's pretty clear that what you think and what is true are two very distinct sets.

[keen marlin]

Thanks cause this made me laugh today

[keen marlin]

So did this

[valid hazel]

So, what I am trying to salvage out of 4 or whoever's beliefs (if we are to be charitable and call them that) is that

1. Space is continuous
2. If space is continuous, it is infinitely divisible
3. If space is infinitely divisible, then infinity is "actual," thus infinitism is true
4. Thus, infinitism is true

The best support I can give for 1 is in terms of the fact our best scientific theories commit us (to my knowledge) to a continuous view on space. GR doesn't make sense, to my knowledge, if spacetime is discrete, since uh, differentials and all. Premise 2 seems to be true, and 3 is dubious for obvious reasons.

[deft quest]

Are the reasons 3 is dubious obvious to a middle schooler?

[valid hazel]

Depends on the middle schooler.

Uh, I can explain more if you'd like.

[deft quest]

I wasn't talking about myself.

[valid hazel]

Yes, but that doesn't mean you wouldn't prefer I explain for others, no?

Such as middle schoolers who you think want to talk about infinitism.

[keen marlin]

No

[valid hazel]

Well, that's quite a shame.

I have no clue what you're trying to say, then.

[keen marlin]

1 and 2 yes not 3

[valid hazel]

I can't get over "realism" in your bio as if it is one specific position.

Are you a realist about everything, haha?

Numbers, God, also nonexistent objects, necessary beings that entail trivialism, et cetera, y'know?

[keen marlin]

Think of it less as dividing
Imagine a cube in your mind
How many squares make up that cube?
I'm not necessarily saying you can divide a cube by aleph 1 and you end up with a square
I'm saying looking at it from an upward perspective (if that at all makes sense) how many squares are needed to become a cube/cuboid. How many of these structures with no third dimension do we need to stack behind each other to give them a finite third dimension
Now back to the cube, let's say it has a width of 1 cm, height of 1 cm, and a length of 1 cm
We have 1 by 1 squares
How do we get that 1 by 1 square to a 1 by 1 by 1 cube?
You're going from 0 to 1
There are the same amount of 1 by 1 squares needed to make a 1 by 1 by 1 cube as there are decimals between 0 and 1
Which is why I said using cantors diagonal theory
The other guy who responded didn't understand my argument
The point is, I understand I might be wrong/ probably am, I'd just like someone to understand my theory before refuting it/ explaining to me why it's wrong

[deft quest]

Meinong's Jungle Book.

[valid hazel]

Yes, well, sadly Meinong gets dismissed without thought because his view seems too absurd to people, since a lot of people are kind of bigots.

[keen marlin]

😭

[keen marlin]

In most of the things I've seen yeah

[valid hazel]

Russell does do a good blow to a lot of the reasons for Meinongianism though.

[keen marlin]

I mean it more in a world politics lense

[deft quest]

I do understand it, and the problem is that 0 + 0 + 0 + 0 + 0 + 0 + ... = 0. Period.

[keen marlin]

😭 You don't

[valid hazel]

Okay, yeah, I still fail to understand this. As TL pointed out earlier, squares do not have any width in at least one direction when projected into 3D space.

[deft quest]

*space, not plane.

[valid hazel]

Ah, thanks

[keen marlin]

I'm just gonna leave it here cause it makes sense in my mind and I'm just struggling to convey it in an understandable way

[deft quest]

The problem is that you're assuming that an actual cube is infinitely divisible.

[valid hazel]

Yeah, so I think you're under the impression squares have some infinitesimal width or something.

[keen marlin]

But I do thank you for saying you don't understand it and that it's not 'not understandable'

[deft quest]

Which is literally the thing you're trying to prove in the first place.

[keen marlin]

? I said 1 cm width

Oh

Bye

I didn't read

[valid hazel]

no dw

[keen marlin]

Infinitesimal is also basically 0

Unless it's a percentage

[deft quest]

No it very much is not.

[keen marlin]

We can debate this if you want

[valid hazel]

What is there to debate over

[deft quest]

An infinitesimal is literally by definition not 0.

It is literally by definition the smallest number greater than 0.

[valid hazel]

Like, it's just false

[keen marlin]

Which is why I said 'is also basically 0'
By definition it isn't, but it practically is

[valid hazel]

Infinitesimals are not additive identities

[keen marlin]

That's like saying 0.9recurring isn't 1 by definition but it basically is

[valid hazel]

It is, by definition, if you actually define 0.999... more precisely (in terms of limits, usually)

[deft quest]

You don't get to say "it practically is" when it by definition is not.

[keen marlin]

Which is why I said we could debate it

You're not the penultimate consciousness

[valid hazel]

What is there to debate over? It's just false, no strings attached, unless you're going to bring in some weird verisimilitude notion here.

[deft quest]

There's no point in a debate about the definition of a concept!

You haven't even taken calculus! What do you know about infinitesimals???

[keen marlin]

I don't think you understand what a debate is
You think it's false
I think it's true
That's quite literally the concept of a debate
Not to mention how abhorrently fallacious you guys' stance is

[valid hazel]

Eh, most calculus is not non-standard analysis, TL.

Most calculus students don't know anything about infinitesimals either. They're just a nice intuitive shorthand for doing limits, generally, almost never are they formalized.

[deft quest]

That was more "you're so far below the level where you would know anything about this", not "you haven't taken the specific class that would teach you about this".

[valid hazel]

Ah.

[keen marlin]

What is up with the aggressive comments along side the ducking..
If you think you're so right then why not agree to debate this?

You think you're right, I think I'm right, let's debate it

[deft quest]

Because literally your position in the "debate" is that the definition is wrong.

[keen marlin]

[valid hazel]

I mean, I don't think I've been rude to you much, 4.

[keen marlin]

So then it would literally be easy to debunk me..

[valid hazel]

Yes, which TL has just done.

[keen marlin]

I wasn't talking about you don't worry
You've actually been really nice

[deft quest]

Which I've done! Like five times! And it hasn't stuck!

[keen marlin]

I haven't given my entire argument

Which is why I asked to debate it

[deft quest]

Who's stopping you???

[keen marlin]

I'm asking to debate it with you

[valid hazel]

4, infinitesimals are kind of an abstract mathematical notion, I don't know if you're trying to tie it to something more physical in nature, by infinitesimals are defined in such a way that they do not resemble zero in any non-negligible way structurally.

[keen marlin]

I agree with you in a sense

I just don't think it's entirely correct

[deft quest]

What the fuck does "penultimately correct" mean???

[keen marlin]

I don't think it's entirely correct

[deft quest]

That's not remotely what the word "penultimately" means.

[valid hazel]

In second place for correctness, I presume.

0 is typically supposed to be defined such that for all a, a + 0 = a, no? However, a + epsilon (where epsilon is some infinitesimal) does not equal a.

[keen marlin]

No I know I have no clue why I said that

[deft quest]

I have no clue why you say anything I've seen you say so far.

[valid hazel]

Eh, you mixed up ultimately and penultimately, which happens, don't worry about it.

[valid hazel]

Sometimes it is useful to abstract away details like negligible factors and ignore them, but in some metaphysical context, this doesn't make much sense to do.

[keen marlin]

I think there's a difference between 0% and an infinitesimal percentage
I don't think an infinitesimal decimal is different to 0

[valid hazel]

You are right than infinitesimals have the nice property that a + k*epsilon for any natural k is always less than a + j for any real 0 < j.

[deft quest]

See, the fact that you would say this, as though you perceive a percentage as something other than a number, just says it all.

[keen marlin]

I find it frustrating that I see you haven't understood my argument yet you disagree
Instead of asking me why, you just go straight to disagreeing
Which is why I asked how old you are cause you don't seem very intellectually mature

[valid hazel]

I don't see how this indicates they think percentages are something other than a number.

[valid hazel]

an infinitesimal decimal is different to 0
what is an infinitesimal decimal?

[deft quest]

Why do you assume I haven't understood your argument?

[keen marlin]

I'm going out now but I can explain why I think that later

[valid hazel]

Infinitesimals do not have decimal representations in the usual sense.

[keen marlin]

Because you're disagreeing and I haven't elaborated enough for you to have understood what I mean...

[valid hazel]

Hey, if you would like to elaborate sufficiently, just write one long post when you get back.

[keen marlin]

Okay can you explain, in your own terms, what you think an infinitesimal decimal is so when I come back I can read cause I think you're intelligent
To me, an infinitesimal decimal would be 0.0(infinite 0s)1

[deft quest]

Have you considered the possibility that I disagree because what you've already said is wrong, and therefore nothing that follows from it can be true?

[valid hazel]

If then, still, I or TL (if they still are entertaining this discussion, which they have no obligation to) do not understand, then it is probably because of an issue on your part, frankly. I do not think it's because TL is dumb or something.

[keen marlin]

Totally fine

[deft quest]

To me, an infinitesimal decimal would be 0.0(infinite 0s)1
Cool, that's wrong.

[valid hazel]

It's uh, not necessariy wrong since they have yet to really explain what that means.

[ruby cairn]

How about the inductive type definition of the naturals in lean. Would that be a finite object or an infinite object?

[keen marlin]

Thanks

Anyway

I'll come bacj later

[deft quest]

They haven't taken calculus, they have no intelligible concept of what it means!

[valid hazel]

Yes, since people do not come up with ideas on their own, I'm sure.

[deft quest]

It's not even intelligible! The closest analogue would be lim_(n -> inf) 1/10^n, which is just 0.

[valid hazel]

Well, again, we don't know what they mean.

[deft quest]

They literally said they're not old enough to have taken calculus.

[valid hazel]

As I commented earlier,

Infinitesimals do not have decimal representations in the usual sense.

[ruby cairn]

Have you seen "Sheafification of g" youtube videos?

[valid hazel]

I'm sure they will enjoy covering sheafs. How about we teach them about Ext and Tor too! /j

[deft quest]

You're literally talking to a self-described child.

[valid hazel]

I do not think bringing age into the discussion for frankly no reason. Some children are precocious, and it really just serves to enforce stereotypes about children rather than accomplish anything at all.

[ruby cairn]

I have only seen the ordinal videos

[valid hazel]

I have not seen anything by this "sheafification of g" fella.

[ruby cairn]

https://youtu.be/dFsa4VeZ0cU?si=fNAKyB2k5HcUMU0Y

[deft quest]

They're the ones who brought it up for no reason. I didn't ask, they just acted like I was bullying a child for telling them they were wrong about their incomprehensible gibberish.

[valid hazel]

This looks like a channel I would not enjoy watching.

[ruby cairn]

How so

[deft quest]

What the heck is an "infinite number"?

[valid hazel]

I think they mean there are infinitely many numbers that have only finitely many digits, but I'm not sure, maybe they clarify in the video.

I'm not going to watch it, since it seems like something that'd give me anxiety and is probably a load of pop mathematical hogwash, to be frank.

[deft quest]

From the thumbnail, it looks like they're talking about numbers with infinitely many digits.

[valid hazel]

Then uh, yeah, you'll probably have to watch their content to find out.

[ruby cairn]

It's about ordinals

He presents it in a way enjoyable for skibidi toilet watchers ig

But the mathematical content seems correct

[valid hazel]

Okay, so from the 2 minutes that I watched of this guy, he is basically just using some intuitions about ordinal numbers and not formalizing anything, which is frankly fine, since it is targeted at "skibidi toilet watchers."

[ruby cairn]

Yea