Is 1 = 0.999... ? Really?

So Magnus…

Here’s my argument:

The “highest order of infinity”, is my cheat:

1.) rational number
2.) uncounted infinity
3.) different rational number
4.) different uncounted infinity
Etc…

I’m not listing the numbers here, just the concepts.

When you divide the interpolated orders of numbers, you get:

1.) rational number
2.) 0
3.) rational number
4.) 0

Etc…

Also!

1.) 0
2.) uncounted infinity
3.) 0
4.) uncounted infinity

Etc…

No matter how many times you divide it, they are still in correspondence. Mathematicians use abstractions to make their proofs. This is a symbolic abstraction (I’m not listing numbers themselves). Symbolic abstractions are fair game in mathematics!

My other argument against you is the dimensionality argument.

You claim planes are infinitely larger than lines.

That’s not true.

A 2D image can not only appear to be moving (3D), but can also render 3D images. Unary can do the same for 2D images. I can link some of these “optical illusions” if you like.

What this means is that a plane is not bigger than a line.

Those are my two arguments against orders of infinity.

Once you “cry uncle” submit, I can start debating Silhouette on 0.999… /= 1

You are probably right.

(N = {1, 2, 3, \dotso})

Sets have no order but we can take a set and arrange its elements in a sequence.

((1, 2, 3, \dotso))

This is a one-directional sequence that has a beginning but no end. So here, there’s no last element, and hence, no infinity-th element.

But this isn’t the only kind of sequence there is. Here’s a one-directional sequence that has an end but no beginning.

((\dotso, 3, 2, 1))

There is no first element but there is a last element and this last element occupies infinity-th position in the sequence.

How about a two-directional sequence that has both a beginning and an end?

((1, 3, 5, \dotso, 6, 4, 2))

First, second, third, etc. But also infinity-th, (infinity - 1)-th, (infinity - 2)-th, etc.

The position that the number (2) occupies in this sequence is an infinite number of positions away from the first position, so we say it occupies infinity-th position.

What I believe this illustrates is that an end in one regard is not an end in all regards. Every single one of these sequences is an infinite one in the sence that it is made out of an infinite number of elements (the number of elements has no end) but some of them have an end in the sense that there’s a last element in the sequence and some don’t.

So yeah, I’d say that infinity can also be used as an ordinal number.

But what about (1 + 1 + 1 + \cdots)? Does it have an end? The visual representation suggests that it does not.

I don’t like that this thread is making me want to sniff paint.

Enough excuses! With philosophy it’s “it’s all pointless,” with chess it’s “I don’t have time to practice,” with math it’s “I sniffed glue.”

I was frankly gifted at math in school. As the topics got more complex though and teachers lost their ability to actually understand them, so that it increasingly became about memorizing operations, I began to loose interest.

I’m honestly grateful. There is an internal logic to math that has an incredible pull that can engulf a mathematicion more perditionously than WoW will a nerd. Without ever knowing what math is, or why it pulls. Questions…

ONLY PHILOSOPHY CAN ANSWER

Magnus you’re playing disingenuous games with infinity here:

1.) you use it as a solid object when it suits you
2.) you use it as a procedure when it suits you

0.0 …123 is a PROCEDURE, yet, I’ve heard you several times in this thread (for different arguments) define infinity as only an object!

You need to make up your mind! It’s impossible to argue someone switching back and forth, especially, if they don’t acknowledge it!

Let’s be clear on one thing:

Philosophy is a radically new thing, which began in Greece. The philosophical texts we have from that time are more sporadic reflections of it than philosophy itself.

Before Greece NOTHING LIKE IT EXISTED.

It is unlike and stands appart from all other things. It is incompatible with any other form of thinking.

Deleuze’s great crime was spiritualizing philosophy. Ain’t nothing spiritual about it. Baudrillard knew this, and found a way out.

He duped, co-opted Guattari. Guattari was 0 spiritual by hos own path. That’s what drew him in about Marx, his rigorous pseudo-science. He was all Das Kapital, 0 Communist Manifesto. But that’s how they do it don’t it? They give ypu the rigour and then draw you into the spiritual…

There is nothing natural, or inevitable, or universal, about philosophy.

I knew Capable was a serious philosopher when he dedicated an aphorism to his suspicion of adjectives. He did so not inspired by, but parallel to Nietzsche. That’s a philosopher.

There is nothing philosophy is for, and philosophy is for nothing.

But we will still conquer the fucking world for it.

A similar argument can be made against you (and your ilk.) Namely, the reason you don’t believe that infinities come in different sizes is because when you take (1 + 1 + 1 + \cdots) and add (1) to it, you get confused by the result because it looks like what you started with – which is (1 + 1 + 1 + \cdots). Failing to understand that you’re dealing with one and the same symbol representing two different things, you conclude – erroneously so – that all infinities are equal. Deceived by the appearances, the accuser is revealed as being guilty of their own accusations (: Accuse the other before they accuse you. Is that a motto of yours?

(0.\dot01) is not a quantity smaller than “it is”. It’s not a quantity smaller than itself.

We’re talking about (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots). Every partial product is greater than zero, thus, the result of the infinite product is greater than zero.

We’re talking about every partial product of (0.\dot01). Not merely a subset. And each one of the infinitely many partial products is greater than (0). That’s how you know the result of the sum is greater than (0).

It’e enough to prove that the gap exists. It’s unnecessary to know its exact value.

There are people who talk the talk and then there are people who walk the walk.

Nothing to do with epistemology.

That’s why I’m saying that you (and Gib) are conflating empirical matters with conceptual ones.

The question is not an empirical one. We are not asking “Given two infinitely long pipes, how can we determine whether they are equal or not?” We are asking “If there’s an infinite number of green apples in front of us and we add a red apple at the start of the line, and nothing else changes, is the number of apples greater than it perviously was or is it the same?”

We don’t care about the poor guy who knows nothing about the situation. Why do you insist on listening to what a clueless guy has to say? Of course, since he’s clueless, he’ll tell you the line didn’t change. But that doesn’t make it true.

“with the exception of the principles of mathematics which i will develop, the philosophical nonsense i learned and adopted from the egyptians will no doubt be attributed to me by me fellow countrymen, and yet i will not let this prevent me from expanding it further into realms of nonsense so immense as to be incomprehensible by modern men lest they be educated by plato, another greek space cadet who is about to go viral.” - pythagoras, ‘the lost chronicles

okay that was funny.

i don’t know how many different ways i can say this my dude, but the stuff that the word ‘philo sophia’ means and represents did not begin with the greeks nor does it belong to them. the word does, but not the stuff. all this eurocentric bias in the western world about the ‘fathers of philosophy’ is nothing more than a fetishsized trend that exists because it has no competition… because what philosophical speculation by other people that did exist in writing didn’t survive the centuries like the greek shit did. and you don’t need to be a historian to realize this. all you need is the most basic of anthropological insight to deduce that any ancestor after the neanderthal and with a ‘modern’ brain, was capable of asking stupid questions just like the greeks.

you’ll understand eventually. in the next thousand years or so the human species will undergo neurological changes that will, literally, prevent them from asking those same stupid questions. we’re starting to see this new, improved human being appear even today. we call them nihilists, which is code for ‘wtf are you talking about? are you high?’

here’s a suggestion for ya. it could very well be the case that philosophical questions which haven’t been answered for two thousand years might not be a real questions. just a guess, though.

I don’t know why you say that you agree with
$$\infty+1=\infty$$
when you really only agree with
$$\infty_0+1=\infty_1$$

:confused:
Who knows what $$\infty_0$$ amounts to?

and that’s just the excuses i come up with for not doing things i’m not good at. you ain’t even seen the excuses i come up with for not doing shit i am good at.

Okay, so we have two identical infinite sets (A = {0, 1, 2, 3, \dotso}) and (B = {0, 1, 2, 3, \dotso}).

In which case we have (B’ = {0, 0_{+1}, 1_{+1}, 2_{+1}, 3_{+1}, \dotso}) which has more elements than (B).

And that’s not the case.

Not true. There is no one-to-one correspondence between the two sets. What you’re doing here is called magic trick.

(A = {0, 1, 2, 3, \dotso})
(B = {0, 1, 2, 3, \dotso})
(B’ = A \cup {0_{new}} = {0_{new}, 0, 1, 2, 3, \dotso})

You do.

Actually, it is what you’re doing (i.e. listening to Cantor) that is giving the appearance of one-to-one correspondence.

That’s true but that does not mean that infinities are equal.

It’s true in the sense that if you have an infinite number and you add 1 to it, you get an infinite number as a result (not necessarily the same infinite number, but still an infinite number i.e. not a finite number.)

On the other hand, if (\infty) represents one and the same infinite quantity on both sides (and wherever else it appears), the expression is false.

Lol @ eurocentric bias. Alright there Greta.

Don’t break your back bending over backwards like that. For them there explanatuons.

Ha ha
yeah Im still waiting to hear those.

“And my ilk” :laughing: here comes the segregation by dissociation language for easier demonisation and premature dismissal…

I don’t have any mottos, no. It’s ironic that you were falsely accusing me of assertion rather than explanation before I pointed out your hypocrisy, and now you’re accusing me of “accusing the other before they accuse you” :smiley:
But it’s been projection of your insecurities onto others from the very beginning - very human of you.

I’ve repeatedly denied the equality of infinities - and you conclude that I conclude that infinities are equal.

Your symptoms of irrationality are really shining through now, if they were merely prevalent before - they’re brazen now.

You’re not only getting deceived by appearances but even hallucinations now!

Again, the point goes straight over your head… :icon-rolleyes:

It has to be a quantity smaller than itself to be valid, which is invalid, making it invalid either way. It’s a contradiction in notation either way - it’s logically not a possible quantity.

So even this contradictory “quantity” is too big to fill the gap between (1) and (0.\dot9) - any possible concept is too big. It literally defies its own existence as soon as any existence is proposed. Zero possible existence resolves to non-existence and therefore no gap. It’s very simple, but simple logic seems a little beyond your skills.

Every partial product is greater than zero, yes - because it’s only partial! Thus the same logic carried over to any “non-partial-product” of some kind of “infinite product” is invalid. Again - poor logic skills on your part.

Partial products of this contradictory and fictitious “quantity” of (0.\dot01) are the completed set. They just don’t include any contradictory and fictitious “non-partial-product” because you never get to one for an infinite product.

You’re trying to pretend you know your way around these mathematical terms and it’s just annoying because you so plainly don’t! #-o Stop embarrassing yourself.

The fact that it’s impossible to narrow down any possible value should ring alarm bells that this “proof that the gap exists” is flawed.

I’m showing you where it’s objectively flawed. It’s not like you have any stake in this trivial topic that’s already been answered - why have you become so emotionally invested in it? You owe it nothing, it’s not part of who you are - it’s just an amusing riddle to occupy amateurs for a bit until they realise that the proven answer teaches them a lesson about judging books by their cover…

I’m still waiting on Ecmandu to teach me something about his Convergence Theory and how he’s using the basic concept of carrying differently to come up with such strange series of equations. I told him very clearly I want to learn about this.

So I’m walking the walk - though I already learned this topic. I’m getting nothing out of this if I don’t help to teach you anything. Maybe you’re angry at me coz I’m so much smarter than you and you’re rejecting my lessons out of spite? I don’t know, but it’s petty whatever your reasons.

It would be so convenient for you if matters of knowledge didn’t apply to you for this thread, huh?

You’re resorting to nonsense about conceptual matters being separate from empirical matters because deep down you recognise the only “traction” you have left on this issue is to insist that your argument doesn’t “need” to be testable.

The reason we care about the poor guy who wasn’t there when you added or did whatever finite operation to infinity, is not to simply “take his word as truth”, it’s because whatever his perspective is it highlights something fundamental about information theory - and we’re dealing with information here. You don’t want to care about him because unfortunately for you, information theory is inconvenient for you and undermines your point. Your resort to deny any and all contradictory evidence to your argument is just “confirmation bias”. I know it’s difficult to admit you’re wrong, but at least you’ll escape this debate with respect if you learn how to overcome your emotional shortcomings that are currently denying you of any integrity and authenticity.

Correct! Progress?

If you want to display it like that, sure. It’s the same as B (and A) either way.

I mean, it literally necessarily is the case by definition - you even accepted the fact that they are identical sets insofar as they have one-to-one correspondence.

As soon as I construct it in a different way to give the illusion that there is no bijection (or that there is “injection” in this case) the identical sets actually objectively lose their bijective correpondence?
From the very start the first terms correspond perfectly with one another. As do the second terms and so on forever… where is the extra element in B? At the end of the infinite set?? We covered this already, Magnus #-o

Why does B’ now have an extra 0?!

You’re accusing me of a magic trick??? I think you’re getting confused with yourself again. This is you literally conjuring something from nothing.

I mean, maybe you meant (B’ = {0_{new}, 0_{+1}, 1_{+1}, 2_{+1}, 3_{+1}, \dotso}) ?
Either way this simplifies as (B’ = {0, 1, 2, 3, \dotso}), which is identical to both B and A as you accepted from the very start…

Really? :laughing: Where exactly? This is more of your mysticism around the “conceptual”, which is “beyond epistemological concerns and doesn’t require testability”, right? Keep that to the religious subforum, buddy - this is math. You need comprehensive proofs, which are not incidentally way beyond your ability.

Listening to the guy who first invoked the notion of 1-to-1 correspondence in the first place, when dealing in matters of 1-to-1 correspondence and how it works - according to its inventor… this sin is just like going to school, right? Unforgivable!
The first element in one set corresponds with the first element in the other set and so on, perfectly, forever… that’s not an illusion :laughing:

I think you’re done, don’t you?

Take a break. Relax. Mull it all over - it’ll be good for you.

What makes you think that only empirical claims are testable? Mathematics is not an empirical science, and yet, it’s perfectly testable. “2 + 2 = 4” is not an empirical claim, and yet, it’s perfectly testable.

I never said nor implied that this thread is about untestable claims. I merely said that it’s not about the kind of questions that you (and Gib) have been obsessing over ever since you joined this discussion.

This thread has nothing to do with science, epistemology and information theory. It has to do with mathematics and logic.

Because that’s what you’re doing. You’re creating a new set, (B’), by adding (0) to it (the extra (0) you speak of) and then by adding all of the elements of the set (A) while relabelling them in order to make the resulting set (B’) look identical to (B).

(B = {0, 1, 2, 3, \dotso})
(B’ = A \cup {0_{new}} = {0_{new}, 0, 1, 2, 3, \dotso})
(B’ = {0, 1, 2, 3, 4, \dotso})

In the final step, you’re renaming (0_{new}) to (0), (0) to (1), (1) to (2), (2) to (3) and so on. That’s how you create the illusion of one-to-one correspondence between the two sets.

It does not simplify. When you write it like (B’ = {0_{new}, 0, 1, 2, 3, \dotso}), it’s pretty obvious that (B’) is greater than (B) because it has all of the elements that (B) has plus the new zero you added. But when you “simplify” it, you make it look as if they are identical. That’s the trick.

So where’s the extra element in (B’)? Well, (0_{new}) is the extra element. Don’t conceal it and you’ll see it.

That would be you.

I forgot my other argument:

If you add a 1 at the front, you have bumped the entire infinity up 1 space, which is exactly the same as adding a 1 at the end (both of which means the series wasn’t really infinite to begin with)

I’m sure I have more, but these three should suffice.

Every partial product of (0 \times 0 \times 0 \times \cdots) is equal to (0) and that’s precisely why its result is equal to (0).

The same does not apply to (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \cdots).

Who told you it’s impossible? I said it’s unnecessary.

It’s because you’re a confused and at the same time conceited mind (hence your defensiveness.)

I accepted that (A) and (B) are identical, not that (B) and (B’) are identical.

Yes, it will be good for you. If anything, you’ll be less focused on who you are in relation to other people and more focused on the actual subject.

Can you do this for us, please?

Or do you REALLY have to tell us how great you are each time someone says something negative about you?

(0.\dot01) is a number that is greater than (0) but smaller than every number of the form (\frac{1}{10^n}) where (n \in N).

That’s what (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots) means. It is telling you “This is a number greater than (0) but less than (0.1) and (0.01) and (0.001) and (0.0001) and so on”.

You can say “But there is no real number that can represent such a quantity!” to which I can respond with “But the set of real numbers is not the set of all quantities.” I can then add that numbers are merely symbols invented by humans in order to represent quantities that are of relevance to them. They are not quantities themselves. Symbols are few and far between, quantities are numerous. And when it comes to quantities, they can be as small or as big as you want them to be. There is no limit.

All in all, all you have to do is understand what that infinite product represents. But you’re refusing to do so, obviously because you have your own agenda – it’s in your interest to misinterpret it.

What’s certain is that (0.\dot01) is not a number that is less than itself. That’s your own invention.

A contradiction would be a statement such as “A number that is greater than (1) but less than (\frac{1}{2})”. That would be a contradiction because we said that a number is greater than (1) (P) and not greater than (1) (not P.)

No such contradiction is committed when we say that (0.\dot01) is a number that is greater than (0) but smaller than every number of the form (\frac{1}{10^n}) where (n \in N). That’s because every number that we say is greater than (0.\dot01) is also greater than (0).

Another contradiction would be a statement such as “A number that is greater than (1) but less than (1)”. A number can’t be both greater than and less than one and the same value. But that’s not what we’re doing either.

Of course, it is possible that we are contradicting ourselves in other ways, by contradicting other statements that we’ve previously made, but the fact is, there are no other statements we’ve made.

The problem with Silhouette is that he’s starting with the premise that there are no numbers smaller than all real numbers. If you START with such a premise, and then you say there is such a number, that would be a logical contradiction. But noone other than him (and those who think like him) start with such a premise.

Certainly not me.

And since this is MATHEMATICS and not EMPIRICAL SCIENCE the only thing we are interested in is LOGICAL CONSISTENCY. You can’t say that some premises are true and others are not. The only thing that matters is consistency: making sure you are not contradicting what you previously stated.

Why would anyone start with a premise that there are no numbers smaller than every real number?

There is LITERALLY no limit to how small a number can be (in your head, of course.) No matter how small a number is, you can always imagine a smaller number. There is no limit whatsoever. All it takes is a statement such as “Here’s a new number N that is smaller than every number that is currently familiar to me!” You don’t have to imagine it or visualize it. All it takes is to state its relation to other numbers.

So what’s the point of limiting yourself to real numbers?

Inability to think abstractly?

Nothing, because I explicitly said that “Most of my objections are actually logical ones, and occasionally I back them up with empirical objections - either way, in order for you to forward your conceptual propositions as knowledge, they need to be testable and tested.”

I never said only empirical claims are testable - you are making things up AGAIN.

Unfortunately you don’t even realise that you have been implying that this thread is about (your) untestable claims at multiple points. Every time you claim you don’t “need” to prove your (il)logical claims, or that the logical arguments of others either don’t exist when they clearly do, or you simply assert they’re false when you notice them whilst at the same time accusing others of that very same fallacy that you’re committing, as well as every time empirical tests are offered to help you understand your errors that you simply claim are irrelevant - you’re arbitrarily invalidating the possibility for both logical and the empirical disproofs to apply to your attempted “proofs”.

Basically you’re constructing epistemological double standards for this thread to make it impossible for validity to prove you wrong whilst simultaneously dictating that invalidity can prove you right. In itself this is fallacious - “moving the goalposts”. This is why you have no intellectual honesty, integrity or authenticity.

Homework for you: devise an argument that would successfully cause you to change your mind that isn’t simply a reiteration of your own points and how you think they’re right.
That is intellectual honesty - the ability to evaluate both sides of the story: the existence of which I’ve been trying to communicate to you all this time.
Obviously you’ve not been in higher education, or you’d be versed in this kind of thinking because that’s what qualifies you for it and qualifies you to succeed in it. Either that or you completely disregard this kind of thinking especially for the internet - but from what I’ve seen I’m going to have to guess you never even made it, and perhaps realised it was never worth you trying. Must be the fault of the institutions though, right? Never yours.

You’re correct that I intentionally add an extra (0) to (B).
You’re incorrect that I’m “relabelling” the elements of set (A). I’m adding (1) to each of their elements and appending the result to the (0) that I first append to (B’). The fact that this makes them identical to (B) is no accident - this was intentional to show you that alternative set construction to end up with the same infinite set doesn’t objectively change the set even if it now “looks like” injection when in fact set identity ensures bijection.

Obviously my efforts were yet again wasted.

I use the term “simplify” in the technical sense of making absolutely no change to the essence of the contents, not colloquially such that it potentially implies concealment or trickery. My terminology is wasted on you.

(B’) has all the elements that (A) has, with 1 added to all of them before they populate (B’) - to the preliminary ends of ({1, 2, 3, \dotso})
That’s why I add (0) first so that this set starting from 1 is appended to a set that has (0) already prepopulated within it.
I defined (B’) as ({0, 1, 2, 3, \dotso}) - stop pretending I didn’t and actually read my explanation. No trick.

The only “trick” is if you mistake bijection for injection because of the intentionally alternative appearance of (B’)‘s construction compared to (B) (and (A)) to conclude that (B’) now has more elements when if you follow each corresponding element to infinity it’s literally impossible to find any injection.

I wish it could be, but unfortunately I’m waiting on you. I won’t give up until you’ve learned something: you the self-confessed non-mathematician professing mathematical expertise.

What would you most like to take from this thread? Victory? Self-improvement? Reconciliation? Teaching your expertise? Name it.

I can repeat myself too if you want.

That’s not getting us anywhere though is it.

I know every partial product is greater than 0. This just panders to your appeal to finitude that you keep denying you’re doing.
INFINITES. We’re dealing with them, not “partial, finitely somewhere along the way of an infinite series” which you’re pretending still counts as valid for evaluating an infinite series.

I showed you that it’s impossible to narrow down any possible value above 0 to fill in any “gap” between (1) and (0.\dot9)
The only value that cannot be divided smaller, thus satisfying this “gap” is 0, otherwise it can always be made smaller.
I’m showing you that it’s literally impossible. You’re just saying it’s unnecessary for it to be possible, but you’re calling it “unnecessary to prove an exact amount”.
The problem is that you don’t appreciate the implications of your vagueness.
This is mathematics, not speculation.

You’re picking up that I’m defending logic and reason huh? Sharp!
Defending myself though? Fuck that - I don’t give a shit what anyone thinks of me unless it suffices as a means to the end of enabling the grander scheme of rationality to be upheld. I don’t want that goal to elevate me or bring me down, it has nothing to do with me - rationality is objective and has nothing to do with the person who forwards it. It works regardless, independently. The only personal satisfaction that I take from philosophical discussion is in the aesthetics of truth. It’s nice. Obviously you don’t think so, but that’s a result of your personal issues and has nothing to do with me personally. Call this kind of dissociation from conceit “conceit” all you like. I give zero shits.

(B’) is defined to biject perfectly with (B), just with alternative construction to make it “look like” it’s different to people fooled by the superficial.
As I keep saying and proving, that’s you.

I’m not giving up on you, Max.
No matter how frustrated it makes me.
I will make you learn even though I’ve been taking the entirely wrong approach of being honest with you about yourself this entire time. I should have been softer and less confrontational - I already knew that this just makes people act irrationally in exactly the same way that you are. I did the same thing with Urwrongx1000 but after a couple of years even he realised I was onto something.

I’m willing to wait that long for you, Magnus.

Oof! If you meant N as (\Bbb{N}) as the set of natural numbers you’re in danger of starting to sound like you’ve been studying up on the subject!

Now we just need to eliminate your reliance on the invalid term (0.\dot0{1}) and maybe we can get somewhere?!

Perhaps if we formulate it like “Given the quantity (x) such that (x=1-0.\dot9), (0<x<\frac1{10^n},\forall{n}) where (n\in\Bbb{N})” we might start sounding remotely close to professional.
But I’m just a mathematician, I’m not a professional one, so if anyone wants to correct me with any legitimacy - please feel free. I’m pretty sure there’s a more succinct and correct, purely symbolic way of legitimately expressing that.

But this is just notation - the argument remains that whilst (\forall{n}) where (n\in\Bbb{N}), (\frac1{10^n}-0\gt0), (\prod_{x=1}^\infty\frac1{10_x}\not\gt0)

Basically “partial” products don’t cut it by definition - like we already covered.

I know what the expanded product of your infinite product is intended to represent.
I know that “there is no real number that can represent such a quantity” - as you say.
It is therefore your duty to comprehensively a valid population of quantities that satisfy the ability to exist between (0) and the difference between (1-0.\dot9)
You need to stop cowering from the formalisation of such a proof, apologising that it’s “not necessary” by virtue that it “ought” to follow from what you regard to be a valid argument, which I have proven to be logically invalid.
You need to do better.
The Hyperreals already attempted this way before you, but as I’ve argued their conflation of the infinite with the finite is only a useful tool rather than truth.

It’s not enough to say that “there should be some quantity there”, you need to validly justify it - my “agenda” is with intellectual rigor ONLY. I don’t give a rat’s ass about anyone’s excuses to get around that - I will hunt down your mistake and destroy it. It’s fun and I enjoy the aesthetics of the result, but I don’t care one jot what form it ultimately takes - even if it turns out you’re ultimately right somehow.

It’s a fact that (0.\dot0{1}) is a contradiction regardless of the fact that it was me who identified it. You cannot logically declare an infinite series of zeroes entirely bounded by a decimal point and a (1) because entirely bounded contradicts the boundless quantity of zeroes in between. Simple. Logic.