/lit/ - Literature

[Anonymous No.15120730]

would Hegel say that 0.999... = 1 or 0.999... =/= 1?

[Anonymous No.15120735]

He wouldn't care and think about something more important.

[Anonymous No.15120746]

>>15120730
he would talk about the metaphysics of =, which he interprets as two lines having a dialectic merger later on.

[Anonymous No.15120759]

>>15120730
the former

[Anonymous No.15120906]

>>15120730
both

[Anonymous No.15120910]

>>15120730
i think he simply wouldn't understand the question and accuse you of being a satanic tempter.

[Anonymous No.15120987]

>>15120910
wrong
>'I cannot pass over without a comment on old Hegel, who they say had no profound mathematical scientific education. Hegel knew so much about mathematics that none of his pupils were in a position to publish the numerous mathematical manuscripts among his papers. The only man to my knowledge to understand enough about mathematics and philosophy to be able to do that is Marx.' [Engels, Letter to A. Lange, March 29, 1865]
>>15120746
this is the correct answer, Hegel believed that deriving calculus from simple arithmetic is a futile effort as the most complex quantities arithmetic operates with are the rationals and the leap between arithmetic of rationals and infinitesimal calculus of the reals (that is a change of quantity) must entail a leap in the metaphysical meaning of the "=" sign (change of quality)

[Anonymous No.15120992]

>>15120730
Hegel negates the Truth so who cares

[Anonymous No.15121016]

>>15120730
0.999...=0.999...

[Anonymous No.15122106]

bump

[Anonymous No.15122218]

[Anonymous No.15122389]

Not sure of Hegel's position on it specifically but the rare few people who study the philosophy of math outside analytic departmental frameworks would say that 0.999… = 1 is the result of trying to reconcile discrete and continuous intuition of units. It's the same problem as squaring the circle or as Zeno's paradox. There are two different ontologies operative that don't play well together.

The question "how complex a polygon do you need until it becomes a sphere?" is meaningless, and creating a special notation to indicate that it "approaches infinite spherishness" and that this approach to infinity equals infinity is only meaningful in a PHYSICAL framework, where infinitesimal approximations are extremely useful because 0.999 … = 1 might as well be true. But post-physics math, that is modern math, forgets this practical heritage and comes along and reifies the mathematical domain, assuming it's some kind of platonic realm of pure truth and that mathematical formulae that work (that don't generate disagreement among other mathematicians) are "truths" which are "discovered." So they try to find some all-encompassing logic or ontology of all mathematics that shows its unity, which (again) they already assume from the get-go.

Because the constant transitioning between discrete and continuous quantities is so fundamental to mathematics, one of the very first things that needs doing if you take for granted that mathematics is a unity (which pre-exists human minds and is discoverable) is two reconcile both forms of quantity. This is why calculus was such a massive revolution, because it allowed this to be done in a million different domains where it was instantly helpful, obviously increasing its prestige and the sense that it must be "true." Most of these domains were real world problems, physics and statistics and so forth, but gradually calculus became fundamental to more abstract domains, and mathematics became more abstract and formalist altogether in the 19th and 20th centuries.

>>15120987
Where does Hegel indicate that this is his position? Seems interesting.

[Anonymous No.15122407]

>>15122218
If im reading this correctly it's just a matter of how the terms are defined in whatever system you're using.

Is there a system in which 0.999 repeating infinitely never reaches 1?

[Anonymous No.15122432]

>>15122407
Sure. But unless you specify the system, 0.999... has a standard implicit mathematical meaning in which it's equal to 1.

[Anonymous No.15122455]

>>15122432
because 'infinity' doesn't mean simply 'keep adding 9s' ? The 'keep adding nines' scenarios seems that it would always be a point off

[Anonymous No.15122462]

>>15122455
Mathematicians nowadays not only assume that the "standard" assumption is that the two are equal, they assume that this is platonically true and how math just "works."

[Anonymous No.15122463]

Read Euler, read Euler.

[Anonymous No.15122475]

>>15122389
Did you study math?

This reads very much like a high-level history of mathematics, which I find very interesting. Are you referencing a specific text with this narrative or is this just a learned agglomeration of math history?

[Anonymous No.15122480]

The difference between .999... and 1 would be infinitely small, but things don't actually become infinitely small in reality, do they? The smallness of something would eventually reach a termination point, scientifically. So either .999... is impossible or it equals 1.

[Anonymous No.15122482]

>>15122455
"keep adding 9s" is not a well-defined concept in mathematics. Just because an expression looks meaningful, doesn't mean it is. You have to define what you mean by every expression.
You could, for example, interpret 0.99... as the formal sequence of digits 0.99...., formally defined as a function f: N->{0,1,2,3,4,5,6,7,8,9,.} so that f(0)=0, f(1)=., f(2)=f(3)=...=9.
You could also define a lexicographical order on such sequences so that 0.999... would indeed (as a sequence of digits) be less than 1.000...
However, such sequences do not define a number system: you run into trouble when you try to define addition and multiplication of such sequences.
The real numbers is closest we got to such sequences but you cannot have a cake and eat it too: to make addition and multiplication work you are forced to identify 0.999... and 1.

[Anonymous No.15122501]

>>15122482
Why do you need to be able to multiply and add the number? Can you not just make a function that says to eternally add more 9s? You will never get to the end of it, but isn't that true of stuff like pi?

Forgive my utter innumeracy I just find the idea interesting

[Anonymous No.15122516]

>>15120730
0.9999999... is just an artifact of the decimal system of representation.
People are so used to the ideia that numbers are unique that numbers with two decimal representations bug them.

>>15122462
Who does that aside from your freshman calculus course?
You might want to take a look at a good calculus book, such as Rudin or Tao's. Hell even baby analysis /rigorous calculus books like Spivak, Courant and Moise make it very clear that you just said isn't right at all

[Anonymous No.15122541]

>>15120730
Bait thread, but Hegel would say 0.999... = 1 because that's what's going to be registered in Spirit. Considering your actions don't have meaningful actuality unless their happening at this level, considering that Hegel thinks being needs to be mediated by its other, the people who are trying to argue using their base intuition that 0.999... =/= 1 are at an infantile stage of the dialectic, they cannot read the language in which the statement "0.999... = 1" has its actuality, and likewise, their garbled "0.999... =/= 1" will remain unintelligible and alien to Spirit forever. It means nothing for Spirit, its the cry of an animal in the dark.

[Anonymous No.15122546]

>>15122482
To illustrate how addition and multiplication goes wrong if you don't identify 0.999...and 1:
Assume that in your number system the usual addition and multiplication work as they do for the rational numbers:
How do you define
0.999.... + 0.9999...?
It cannot be 1.9999... because if it is, you subtract 0.999... and get that 0.9999...=1, which is false.
It also cannot be 2, because then you divide by 2 and also get 0.999...=1
There turns out to be no reasonable choice of definition of addition and multiplication of such sequences.

Keep in mind that what I've shown you is not actually how the reals are constructed. It's merely an illustration to see why even in different number systems, provided nice rules hold for addition and multiplication, you want 0.999...=1.

[Anonymous No.15122585]

>>15122501
>Why do you need to be able to multiply and add the number?
I guess that's just part of the definition mathematicians accepted of what it means to be a number.
There are many other systems that look absolutely nothing like natural or real numbers (for example, p-adic numbers) that are still called numbers because you can add, multiply and subtract them.
It's a convention really.
>Can you not just make a function that says to eternally add more 9s?
Yes. As I said, you can define a function f:N->{0,1,2,3,4,5,6,7,8,9,.} by the formulas f(0)=0, f(1)=., f(n)=9 for n>1.
It represents the formal sequence (0.99999999....).
> You will never get to the end of it, but isn't that true of stuff like pi?
That is true of pi and of many other numbers such as sqrt(2).

[Anonymous No.15122592]

>>15122516
>Who does that aside from your freshman calculus course?

A lot do. Trying to do philosophy or history of mathematics around mathematicians is like pulling teeth. In the daily argument on /sci/ about this topic, every undergrad fag takes for granted that somehow an infinitesimal approaching some number "is" the number. They don't say for the formalist purposes of an arbitrary system that works for doing a great many things, they just say that it "is" what it "is." Then they smuggle this assumption into other domains, including more abstract ones like geometry, so that even mechanically and computationally talented mathematicians go on wild goose chases for decades looking for things they only "know are there" because an arbitrary ontology dictates it.

They do even worse shit, like take set theory as platonically real. Not joking. Even the ones who will begrudgingly admit its unreality and arbitrariness will still cling to it as if it's transcendentally (in the Kantian sense) self-evident or some shit.

[Anonymous No.15122599]

>>15122389
>>15122475
I want to know more about this as well anon. Never thought of it as two distinct ontologies. Any source were I can dive into this subjects?

[Anonymous No.15122616]

>>15122585
Could you explain the difference between pi and the 0.999, why can you add/multiply the former but not the latter? Or is pi also not really a number

[Anonymous No.15122619]

>>15122546
You can have 0.99999 != 1 but that means including infinitesimals in your number system, and although infinitesimals can be made rigorous and logically consistent they also brings all sorts of difficulties.
Plus when people say 0.999... != 1, I don't think they mean "infinitesimals exist".

>>15122501
What are numbers? The natural numbers are a model for counting. The rational are a model for proportion. The reals a model for measuring. The negative numbers are a model for orientation, debts and also complete the other number systems in a useful technical way. The complex numbers are a natural place to talk about polynomial roots while also encoding certain geometrical properties.
All of those things are such that we might want to add and subtract them.

[Anonymous No.15122623]

>>15120730
He looks like Werner Herzog

[Anonymous No.15122639]

>>15122592
Mathfag here, you don't sound like you know a lot of maths. Out of curiosity, what's the highest level of mathematics that you're familiar with? What's a subject that you've been studying recently?
0.9999... absolutely is 1 under the standard definition of 0.9999.... If you've ever read even a chapter of real analysis you would understand this fact.

[Anonymous No.15122668]

>>15122501
>Why do you need to be able to multiply and add the number?

The other guy says it well:
>I guess that's just part of the definition mathematicians accepted of what it means to be a number.

If you want to historicize why it was useful, you can do that. Go look at how Zeno's paradox puzzled people, or squaring the circle. Then imagine that in the early modern period, people were trying to do that same kind of thing, with the same feeling of puzzlement and frustration, but applied to extremely real physical problems, and especially astronomical problems (which need to be able to describe ideal curves whose curviness is determined by variables, in a reflexive way).

Discrete counting is manifestly useful. Can you imagine using only a continuous mathematics, like some ancient and primitive people sort of have, to describe relatively small quantities like 5 fingers or 219 eggs? It's useful to have an arbitrary discrete counting system. But then you run into problems of measurement, first of physical objects, then of intuitive manifolds (geometry). What do you do then? Again, clearly it's meaningful and useful to speak of continuous extension - we need lines that aren't composed of discrete points, just as much as we need "infinitely small" points. When you want to measure the magnitude of a building you've determined is 2 by 2 cubits, you don't have much trouble, but when you want to measure the magnitude of something that invokes pi, which even the ancient Egyptians and Babylonians frequently did, you instantly run into the problem of "what is this number REALLY?" The Babylonians simply fudged it, they said pi was 3. Later people dealt with it in different ways. We deal with it in our own way, one which allows for a relatively formalized arithmetic and a relatively formalized geometry to play well enough together that we can do a lot of things (which have accumulated and been tested over the years as fairly robust).

>>15122639
I don't understand. I said my issue is with the definition being arbitrary and formal, and with people taking it as not arbitrary/formal but tacitly assuming it's part of some ideal structure of pure math in god's mind.

[Anonymous No.15122747]

>>15122616
As I said before, you can multiply both 0.999... and pi (provided you interpret 0.999.. in the standard sense, that is, as the least real number not less than any of the finite truncations {0.9, 0.99, 0.999, ...}, which also makes it equal to 1).
What I said in my post is not that you can't multiply 0.999.. but if you choose to interpret 0.999... in a nonstandard way, a way in which 0.999... does not equal 1, then in that system you cannot multiply or add things. There is simply no consistent way to define multiplication that satisfies the usual axioms of arithmetic.
Both pi and 0.999... in the standard sense are real numbers. You can add, multiply, divide them by any other real number (except, of course, divide by 0).
>>15122619
>means including infinitesimals in your number system
Sure, but it also means getting rid of the notion of numbers as strings of digits.
>>15122668
>arbitrary and formal
That's true, but also IMO the definition is the most natural one. I challenge to give a definition of 0.9999... as a number that you can add and subtract without looking anything up that makes it not equal to 1.
>ideal structure of pure math in god's mind
It is part of the ideal structure of pure maths in god's mind, I think. Why do you think this is an unreasonable position to hold? The definition just tell us what we're talking about.

[Anonymous No.15122756]

>>15122389
>For the mathematically infinite, which emerges in mathematics in the form of the series, the transition of limit, fluxion, differential quotients, the infinitesimal, etc., is no longer something merely quantitative from his standpoint, but already contains a qualitative moment, so that here mathematics cannot avoid the concept, whereas the concept is supposed to be something alien to mathematics, something which is supposed to contradict all its laws, and thus mathematics can only take it in an 'arbitrarily lemmatic way' from a field alien to mathematics. Hegel correctly states that elementary mathematics would never have given birth to analysis out of itself, that it was driven to do so by the requirements of 'application', i.e. of practice, technique, science.
>When Hegel writes: 'The appearance of arbitrariness presented by the differential calculus in its applications would be clarified simply by an awareness of the nature of the spheres in which its application is permissible and of the peculiar need for and condition of this application', (ibid., p.284) this materialist kernel is in completely the same sense as Engels's following claim concerning the material analogies of mathematical infinity:

'As soon, however, as the mathematicians withdraw into their impregnable fortress of abstraction, so-called pure mathematics, all these analogies are forgotten, it becomes something totally mysterious, and the manner in which operations are carried out with it in analysis appears as something absolutely incomprehensible, contradicting all experience and all reason.' [Engels, Dialectics of Nature, p.271]
https://www.marxists.org/reference/subject/philosophy/works/ru/kolman.htm
your comment on Zeno's paradox is spot on and indeed again here the problem was "solved" by mathematicians by postulating the existence of an infinitesimal amount of time where the arrow nevertheless is in motion that is changes it's position but this infinitesimal amount is something different from the zero of time
>Aside from the extremely dubious practical value of this “axiom”, it does not withstand theoretical criticism either. How should we really conceive the word “moment”? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that “moment” to inevitable changes. Or is the “moment” a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom ‘A’ is equal to ‘A’ signifies that a thing is equal to itself if it does not change, that is, if it does not exist.
https://www.marxists.org/archive/trotsky/1939/12/abc.htm

[Anonymous No.15122773]

>>15122592
First, you're wrong. Nobody in their right mind thinks limits mean "just keep adding bro". The notion of limit exists because of the very obvious problems that "just keep adding it up" brings.
Likewise, = is not really equality in the obvious sense you seen to believe. Mathematicians work by, among other things, generalizing existing notions. In different texts and areas equality might mean completely different, much broader, things. In algebra one often takes all isomorphic structures as being the same one, despite the fact they aren't equal in a strict sense.
If you have actually tried to talk to a mathematician, it's likely that either he or she internalized it to a degree were they don't consider it anymore, or they saw you know jack about actual mathematics and just bullshitted something.
Also, most mathematicians don't really care about ontological questions about the objects they work with. If you press then they will either sprout some platonist bullshit or some formalist Hibertian bullshit.
Because ultimately it doesn't matter.

[Anonymous No.15122786]

>>15122747
why does 0.999 need to become 1 to be multiplied but pi can continue on indefinitely and be multiplied?

[Anonymous No.15122813]

>>15122786
0.999... doesn't become anything. It was already 1.

[Anonymous No.15122815]

1,
he's all about taking the bad infinite process and making it into the good infinite through reflection

[Anonymous No.15122835]

>>15122786
I'm having a hard time trying to understand your question.
The whole issue is how you choose to define 0.9999....
There is a choice to be made, because as it stands, unless you define what you mean formally (say, in terms of ZFC), the expression 0.999... is meaningless.
My point is that if you try to define it as the sequence of digits(formally a function), that doesn't work because in such a number system you cannot multiply and add numbers.
Instead, mathematicians chose the standard interpretation to be that 0.999.. is the real number defined as the limit of the sequence (0.9, 0.99, 0.999, ...). As a real number, it is equal to 1.
pi is a real number in a fixed numbers system. You can add and multiply it because you can add and multiply all real numbers. The fact that its decimal expansion is nonperiodic is irrelevant.

[Anonymous No.15122873]

>>15122835
there is no way to get 0.999 as the fraction of two numbers or whatever?

[Anonymous No.15122890]

Also note that even in hyperreals, 0.9999... is equal to 1 because of the transfer principle.
You could, however, redefine 0.9999... to mean the equivalence class in the nonprincipal ultrafilter quotient of the sequence of real numbers (0.9, 0.99, 0.999, ...). Then it won't be equal to 1 anymore because the set of entries where (1,1,1,1,...) and (0.9, 0.99, 0.999, ...) are not equal is cofinite (in fact, its complement is the empty set).

[Anonymous No.15122893]

>>15122873
999.../999...

Or if we simplify 1/1.

[Anonymous No.15122900]

>>15122873
0.999... = 1/1 = 2/2 = pi/pi.

[Anonymous No.15122912]

>>15122893
what about 10 divided by 10.00000000...1

[Anonymous No.15122919]

>>15122912
>10.00000000...1
What do you mean by this expression?

[Anonymous No.15122927]

>>15122912
0.999...9.
What's your point? 0.999...9 != 0.999...

[Anonymous No.15122929]

1=0.999... because the difference between them is 0.000...0001

Theres always an infinitely small one between them which cannot be deleted

[Anonymous No.15122932]

>>15122927
>0.999...9
What do you mean by this expression?

[Anonymous No.15122943]

>>15122929
>0.000...0001
What do you mean by this expression?

[Anonymous No.15122965]

>>15120987
>this is the correct answer, Hegel believed that deriving calculus from simple arithmetic is a futile effort as the most complex quantities arithmetic operates with are the rationals and the leap between arithmetic of rationals and infinitesimal calculus of the reals (that is a change of quantity) must entail a leap in the metaphysical meaning of the "=" sign (change of quality)
Jesus fuck.

[Anonymous No.15122972]

>>15122929
if we assume 0.999... != 1, then there exists some real number between them that's greater than 0, and less than one. Can you define that number?

[Anonymous No.15122989]

>>15120730
He would say that 1x1=2 because how can the square root of 4 be 2 but the square root of 2 not be 1

[Anonymous No.15123008]

>>15122989
holy based

[Anonymous No.15123024]

>>15122989
Hegel was a little bit of a stupid nigger, after all.

[Anonymous No.15123051]

>>15123024
Worse still, he was a g*rm

[Anonymous No.15123068]

>>15122989
What would be the square toot of 3 then?

[Anonymous No.15123095]

>>15122989
based black hegel

[Anonymous No.15123119]

>>15123051
better than being an ang*o or a j*w

[Anonymous No.15123193]

>>15122972
0.999...5

[Anonymous No.15123210]

>>15123193
>0.999...5
That's not standard mathematical notation. What do you mean by this expression?

[Anonymous No.15123241]

>open thread for /sci/ memes
>see a bunch of retards whining about Engels, mathematicians being poopyheads, etc.
>mfw marxoids try to do math

[Anonymous No.15123250]

>>15123241
>mathematicians being poopyheads
wdym. I think my explanations in this thread have been good and accessible to laymen.

[Anonymous No.15123256]

>>15123210
>What do you mean by this expression?
0.999...+0.000...5

[Anonymous No.15123266]

>>15123250
Most layman don't understand even what a definition (in the sense a mathematician might think of a definition) is, or why one might care about such a thing. So no.

[Anonymous No.15123277]

>>15123256
What do you mean by 0.9999.... and what does 0.00000...5 mean?

[Anonymous No.15123280]

>>15123256
>0.000...5
What do you mean by this expression?
>>15123266
>what a definition (in the sense a mathematician might think of a definition) is, or why one might care about such a thing.
That's what I've been trying to explain in my posts.

[Anonymous No.15123312]

>>15123277
>What do you mean by 0.9999....
0+0.9+0.09+...+0.0000...9
>what does 0.00000...5 mean
0+0.0+0.00+...+0.00000..5

[Anonymous No.15123315]

>>15120987
>Hegel knew so much about mathematics that none of his pupils were in a position to publish the numerous mathematical manuscripts among his papers.
what does this even mean? he knew how to take a derivative? philosocucks are required to take 12+ years of math classes nowadays and they still don’t know shit, imagine how bad it was back then

[Anonymous No.15123322]

>>15123312
>>what does 0.00000...5 mean
>0+0.0+0.00+...+0.00000..5
Your definition is circular. I hope you realize this?

[Anonymous No.15123334]

>>15123312
>0.00000..5
Lmao you just said X is X, using a symbol to define itself. I'm not asking about syntax anon. What do *you* understand when you see that symbol?

[Anonymous No.15123369]

>>15122943
Infinitely many 0s then a 1, you mathematical newfag

[Anonymous No.15123374]

>>15122972
You have bad axioms for the real numbers. Dont use dedekind cuts, they're full of BS.

[Anonymous No.15123383]

>>15123334
>Lmao you just said X is X, using a symbol to define itself.
With every definition attempt you either take something as basic and obvious, get the infinite regress or a circular reasoning. Do you have any other way to define things?
>What do *you* understand when you see that symbol?
A number which is the half of the difference between 1.000... and 0.999...

[Anonymous No.15123387]

>>15123369
If there are infinitely many zeros, how can you put a 1 afterwards. An infinite sequence would be without end, and without an end you wouldn't have where to out your 1.

[Anonymous No.15123393]

lads what about 0.666666
does it end in a 7

[Anonymous No.15123404]

>>15123393
No, because infinite Satan can't get lucky.

[Anonymous No.15123445]

Does anyone have that big equation he wrote?

[Anonymous No.15123446]

>>15123387
Is there finite or infinite amount of rational numbers between 0 and 1?

[Anonymous No.15123474]

>>15123374
Can you expound on this or provide some literature in the subject. I only ever took elementary real analysis, and that was several years ago, but I recall this kind of argument being utilized to explain uncountable and countable infinites.

[Anonymous No.15123485]

He said the infinite comes from the finite

[Anonymous No.15123486]

>>15120730
Neither, 0.999... = buy my book

[Anonymous No.15123498]

>>15123474
Don't listen to him, Dedekind cuts is a fine definition of reals.

[Anonymous No.15123520]

>>15123383
Try reading a math book nigger

[Anonymous No.15123527]

>>15123520
Thanks for the admission of defeat.

[Anonymous No.15123560]

>>15123527
You're a literal retarded who keeps restating the same thing over and over again. Refusing to engage with you is as much an admission of defeat as refusing to play chess with a pigeon. Because much like the pigeon you just shit everything up.

[Anonymous No.15123569]

>>15123560
That's quite a long and passionate refusal to engage.

[Anonymous No.15123586]

>>15122786
Because mathematicians have fuzzy notions of infinity, which they import implicitly and unconsciously to handle situations as appropriate. In most mathematical contexts, infinities approaching limits are taken to become the thing they approach infinitesimally, while infinitely repeating "irrational" (literally, cannot be expressed as a finite ratio) numbers repeat their "irrational" procession irrationally.

It's why ideas of infinity, both explicit formulations of it and the implicit assumptions they fuzzily hang upon, are so central to mathematics yet also so murky and disputed.

You might ultimately be interested in intuitionism and more metaphysical/esoteric approaches to math. Just be aware that they are both fringe, the former less than the latter. Most mathematicians don't do true foundationalism, they do pseudo-foundationalism like set theory. They aren't concerned with concepts or intuitions or what math "really" is (even if they occasionally think they are), they are concerned with how a linguistically and culturally stabilized set of definitions functions based on agreed-upon uses of functions generally considered derivable from those definitions.

[Anonymous No.15123621]

Another thought has occurred to me
if 0.999... is 1, then what is the number closest to 1 that isnt 1?

[Anonymous No.15123637]

>>15123621
There isn't one. Why would there be such a number?

[Anonymous No.15123646]

>>15123621
No such a number, because the reals with their standard order aren't a well ordered set. There's no such notion as a next number, nor do open intervals have least or maximum elements within themselves.

[Anonymous No.15123673]

>>15123621
What about 0.999...8? 0.999...8999... if we limit the number of ...s to 2.

[Anonymous No.15123688]

>>15123637
>>15123646
how would you express in mathematical notation the concept of getting ever closer to 1 but never reaching it?

[Anonymous No.15123700]

>>15123688
Why assume mathematical notation is concerned with expressing that? You can see the ontological commitments of modern mathematics here >>15123646 with the idea that the reals aren't a "well ordered set." You are thinking about math as a metaphysical realm and trying to ask about its real qualities, but that's not what this is. Maybe that's what myth really and ultimately is, but it's not what these people find useful or what they create axiomatic systems for post hoc.

[Anonymous No.15123710]

>>15123700
>Why assume mathematical notation is concerned with expressing that?
because it sounds like a mathematical concept? idk

[Anonymous No.15123717]

>>15122546
>How do you define
>0.999.... + 0.9999...?
1.999...89?

[Anonymous No.15123721]

>>15123688
A sequence of numbers a_n gets ever closer to 1 but doesn't reach it if:
The function n->|a_n - 1| is decreasing and a_n != a for any n.

[Anonymous No.15123726]

>>15123721
What do you mean by "for any"?

[Anonymous No.15123729]

>>15123710
Many things that sound like mathematical concepts aren't.

[Anonymous No.15123753]

>>15123729
it's about numbers you fag

[Anonymous No.15123769]

>>15123753
Many meaningful sounding questions about numbers are nonsense

[Anonymous No.15123778]

>>15123315
>t. never read Hegel's Science of Logic

[Anonymous No.15123857]

>>15123710
So are quaternions, but does that mean quaternions are/were metaphysically real?

It's like saying the medieval idea of impetus is real, or the pre-Einsteinian idea of aether is real. Impetus and aether were concepts used to describe and interact with phenomena in the world. They turned out to be wrong, at least by our standards, but people took them for granted because they "did work" perfectly well within the logical/linguistic systems people had created to describe the physical world, until they broke down when new information and conceptions arose.

Think of professional math as a language hovering above a physical world which is itself hovering above whatever math "really" is. This isn't even to say that math as a language (with various uses, abstract and applied) and the mathematical ideal realm will never become coterminous, it's just to say that they aren't currently. Math is a junk drawer that gets reorganized periodically.

[Anonymous No.15123916]

>>15123857
I don't even mean necessarily metaphysical, i have no idea what math is metaphysically. But just conceptually I feel that the concept of number closest to 1 makes sense

[Anonymous No.15124212]

Physics is solved
writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/