what's the minimum thickness of a line? i mean, it can't

>>9152760
a mathematical line has a thiccness of zero

>>9152761
but then wouldn't the space it occupies be zero, contradicting it being a line? its dimension would be zero, but then you say it can map a set, and not just that, but it can fill up spaces and whatever. how is this possible? doesn't that contradict it having a dimension of 0xR?

Alright fine you fucking plebian. There's actual rigorous definitions of how space filling curves work, but you clearly don't know them and I'm not going to spoonfeed you. For your imbecilic, 3-D monkey brain it would suffice for me to just lie to you. So I will. A line doesn't have zero thickness. It's thickness is the smallest positive number greater than zero.
>but that number doesn't exist
You don't even fucking care if it doesn't exist. You can't even prove it doesn't exist because you don't know/care about rigor. You just want to be right and appear smart and curious. You're not curious. If you were you would read. You can learn the magic or you can swallow the bullshit I just fed you. The choice is yours.

>>9152785
man is crazy edgy but hes right

your question is dumb.

>>9152785
>making assumptions about whether i care or not so as to avoid having to actually enforce some sense of knowledge on the topic instead of shitposting.

b8 harder. i choose to keep this discussion open since you failed to answer anything.

>>9152760
Space doesn't factor into geometrical reasoning itself; only in our thinking about geometry. Euclidean lines are defined as breadthless length; certain properties that these abstract entities have are applicable to real world objects.

>>9152766
0^R

>>9152829
im not denything that this is a generalization of what we try to think of as a line, im just questioning how volume comes into play here, if at all.

basically you're saying one of the properties here, its thickness, doesn't exist or is just zero. if that's the case, then its ability to occupy space would be zero because its volume would be zero, which is the same as saying it doesn't exist? if volume doesn't come into play then how does space get involved with it from a structuralist point of view?

>>9152820
He explained why your question is silly and now you're claiming he didn't answer you at all and instead spent your post getting buttmad. Fuck off nigger, it takes more than one person to keep a discussion open by the way.

>>9152760
Limits

>>9152760
It literally has 0 thickness. If you want to know what purpose this serves it is simplification.

To give a trivial example, suppose you have a wire that is charged and you want to compute the electric field around it. Technically this wire is 3 dimensional so you would treat it as a volume, but then you realize that if you use the formula for a one dimensional charged body, the result is pretty much the same. So why even bother getting 3D measurements to then plug into the more complex 3D formula when you could just use the 1D formula.

So a line is an ideal wire that produces 0% error when you use the 1D equation. Obviously wires in the real world will have 0.00000001% error but that is negligible for engineers.

A sphere doesn't exist in our universe. There's no such thing as a perfect sphere, not even the electron is a perfect sphere, so it's just a mathematical abstraction. But, as you can see, we can use its properties and apply it to our universe and it fits well.

>>9152836
I think I understand what you're asking, it's about infinity and the continuous, right? If it's the case, then you should study a little bit of Analysis.
Analysis together, with topology, is probably the hardest thing you'll face in your math course, because it deals exactly with the things you're asking.

Steven Lay is a good book for beginners, and I recommend it for those who are interested on the subject.

>>9152836
How big is the number 1? How much space does it take up? It has to take up SOME space otherwise it would have 0 volume and that's saying it doesn't exist! What about 'plus'? Or how big is 'happiness'?

In case you aren't getting what I'm saying, just because something doesn't take up space doesn't mean it doesn't exist. You're making that assumption a lot so you should at least back it up.

ε

>>9152934
>false equivocating.

>>9152969
The term is false equivalence, and you should at least explain yourself. Assuming you're the OP, you yourself claimed multiple times that having no volume means it doesn't exist, are you backpedaling on that now?

>>9152977
i never claimed that a number has to take up space.

>>9152985
Why does a line need to, but not a number?

>>9152836
No. A Euclidean line has only the property of length. That's what is meant by its having no breadth. It is an abstract entity which can be applied to the real world when talking about lengths of things. Euclidean lines DO NOT exist physically on purpose.

>>9152785
this is a good post
>>9152944
this is the short form of the same post

>>9152985
a line is just a lot of numbers arranged in a certain way

>>9152891
>Fuck off nigger
Why the racism?

1 planck length.

>>9152760
>minimum thickness of a line
You mean lower bound thickness of a line? 0

>>9153667
im mainly a physicist by trade but holy shit why do physicists always find the most inane and tedious answer to every question about arithmetic

>>9153821
Nigga, it's the practical answer, unless there's something smaller.

>>9153839
yeah there is something smaller

half a planck length

and theres something smaller than that too

half a half a planck length

are you beginning to see where physics and arithmetic dont necessarily work in tandem

>>9153839
Planck units are not quanta.

>>9153839
>Nigga, it's the practical answer, unless there's something smaller.
Why the racism?

3(x^2/x^2)

>>9153667
I dunno if you could consider something 1 planck length in width to be a line.

Unless you managed to fill the space to either side of it so the lack of matter in that space created a line.

>>9153635
Nigger is a state of mind

>>9152785
Looks like someone is butthurt he's been shown something he doesn't know.
>>9152789
Questions -- even if it's the top question asked by retards worldwide -- only ever seem stupid to stupid people, save for repetition. Your congitive reaction of "herp that's stupid," is a consequence of not knowing the answer and assuming "welp it contradicts the authority of what i've learned, therefore it's stupid."

I'll tell you a secret: Anyone who absorbs everything they're taught, unquestioningly, are the non-critical thinking idiots in any dialectic.

>>9152760
Lines are an a priori concept that can't be proven to exist objectively, like numbers, and they are just as valid as numbers. Space-filling curves incorrectly assume a space can be filled with infinite iterations of the infinitesimal. It could have practical use, but it would never happen with a real line, because you're right -- they don't exist.

>>9152760
Whatever it is, it's less than ε, where ε>0 is arbitrarily small

>>9154635
Retard.
There are no stupid questions, only stupid people like you who ask stupid questions.

THICC

>>9152760
Do you play board games or card games, OP?

>>9155954
Yugioh, pokemon, and magic the gatering.

>>9155962
Mathematical objects are game pieces in the same way that permanents are game pieces. You define a line to have certain attributes, and each attribute lets different mathematical objects act on it.

So in 2d space, a line has slope. So anything you can do to a number, you can modify the line by changing its slope. But it's not like the line is an actual physical thing, it's just an object with a couple of different attributes you're setting. Just like you don't actually have a red 5/5 Dragon Creature with Flying and Haste, you have a couple of attributes that let the card in front of you interact with the cards around it in well-defined ways.

>>9155973
fun video that talks about what I'm talking about
https://www.youtube.com/watch?v=F_0yfvm0UoU&t=65s

A line is a mathematical concept.
A line does not have thickness.
You have only seen convenient visual representations of this concept.

>>9154635
Questioning what you're told doesn't make you smart, you smug dickhead. Knowing the truth makes you smart. When people want to learn math - and I mean really learn math, not gain some superficial appearance mathematical prowess - they read math books. They don't come to /sci/ and try to argue that certain mathematical concepts are wrong because they don't make intuitive sense to someone completely unaware of formal proofs.

Physically planck lenght. Mathematically none as the line doesn't matter.