## 0.999... = 1

• 8.4k
Indeed. A friend of yore, long departed, would quote Aristotle' point that at some stage all that is left is to laugh and walk away.
It is worth learning just how far @Metaphysician Undercover is willing to go; and how far his pretence of rational conversation drags us into his madness. He should have admitted his error, one supposes - and yet he hasn't, so there must be something he has misunderstood, something that will trigger Meta's realisation... and so the conversation continues.

It becomes harder for @InPitzotl and @jorndoe to walk away the more they invest.
• 4.6k
We all learn that lesson at least in part the hard way. For many men, it's a woman. But in a sense MU has been clear and secured himself in a bombproof redoubt. His is about the metaphysics of math concepts - I do not know what that means - and from there he can throw what bombs he likes. But I agree: it can be hard to disengage from crazy-making.
• 21
MU has made it completely clear he's a nut-case, and not even an honest nut-case, yet some people don't get it. And a parallel with Trump and similar people. The right approach to them is to treat them appropriately.

I disagree. Just because he's illogical doesn't mean his psychology isn't interesting. He's yet to answer the question I posed most likely because it isolates the underlying hypocracy of his debate stance -- apparently truth has little to do with his posting motivation -- so it's only pointless to argue against that which his hypocracy is productive of. His whole intellectual orientation is faulty. But it's for some reason been useful enough for him to maintain it.

Something tells me that it's partly solipsism, partly an expression of aggression against the imposition of an external control over his thinking. So he's in company with the likes of Kanye West when he decided to support Trump after the media made out it was a bad choice.

People like this aren't nut-cases; they're protesters.
• 8.4k
...from there he can throw what bombs he likes.

Yes, it's about vulnerability, not truth. Meta sees his argument as invulnerable, others see it as contradictory and infertile. More over the dance gets attention.

I think you are being needlessly complicated. He's simply seeking attention, and his approach works well.
• 21
Na, I'm just mining it for knowledge rather than being an asshole.
• 358
So basically good enough being good enough. To most. Sure. Right?

I mean you don't typically use mathematics for no reason there generally is a precision that is lost otherwise that is fundamentally detrimental but.. for most yeah why not.

I pay for a 15 minute massage and for some reason I time it and it only turned out to be 14 minutes and 59 1/2 seconds. I wouldn't call that a scam or even anything.

Again mathematics generally has a purpose. It's not like fashion. Say I pour you a glass of water. Nice of me, right? Now if I put- pay attention now- less than a billionth of a gram of polonium in it. You would be dead in minutes. Just saying.
• 1.5k
I pay for a 15 minute massage

I haven't checked out this thread in a while, sounds like it's about to get spicy. Alright!

Again mathematics generally has a purpose.

You're confusing pure math with applied math. A common category error. Math is not subject to any standard of applicability. On the contrary, the only criterion for the worth of a piece of math is whether it's regarded as interesting and beautiful by mathematicians. But to satisfy the Philistine in you (one with no appreciation of the arts), be aware that the most abstract and useless mathematics of one era often becomes a core engineering discipline of another. Number theory provides a striking example. Regarded as supremely beautiful yet utterly useless for over 2000 years; number theory is now the foundation of Internet security and cryptocurrencies. Mathematicians let their minds wander, and they let others care about purposes.
• 255
Something tells me that it's partly solipsism, partly an expression of aggression against the imposition of an external control over his thinking.dex
MU has a metaphysical theory of numbers, he's a believer in them in the full b-word sense (it's part of his identity... almost literally), and modern math is kind of a heresy wrt it. That's my take. I personally envision his theories as being roughly of both the form and value of Eric the half a bee.
• 1.5k
MU has a metaphysical theory of numbers

I can't help being struck by the amount of mindshare @Metaphysician Undercover holds here.
• 8.4k
Eric the half a bee.

Cyril Connolly?
• 21
MU has a metaphysical theory of numbers, he's a believer in them in the full b-word sense (it's part of his identity... almost literally), and modern math is kind of a heresy wrt it. That's my take.

That makes sense. The arrogance is still pretty weird, though. All the same, math noobs like myself can learn a bit from the counter-effort. This thread was a heck of a read.

I personally envision his theories as being roughly of both the form and value of Eric the half a bee.

LOL
• 7.2k
In that case, may I ask why you're arguing your position here? If you yourself can't be persuaded by others, what makes you think others will be persuaded by you?dex

I partake in this forum to learn, and to help others learn. Learning is a communal process requiring sharing and consent. I apprehend a difference between understanding and being persuaded. One can very often persuade a person to act in a particular way, without the person understanding the need to act that way, or the reason why that action is being called for by the other. This difference is what allows for the existence of deception.

"Learning" is a broad term which is used to refer to both, understanding, and being persuaded to act without understanding. So for instance, as children we are highly susceptible to being persuaded, and our capacity for understanding is quite limited. We are taught principles, like arithmetic, and are persuaded to behave in a particular way, without understanding the reasoning, which is the theory behind those principles. "Learning rules" of arithmetic, and even the "rules" of higher mathematics is not actually a case of understanding principles, as "learning rules" seems to imply. Fundamentally it is a matter of being persuaded to act in particular ways in response to specific situations, and develop particular habits, like training a dog. We are persuaded to act in a particular way without understanding any actual rule, though the rule might be produced as a description of that behavior. Wittgenstein is relevant here. When we are older, and our capacity for understanding is increased, one might delve into theoretical mathematics, what fishfry called pure mathematics, in an attempt to understand these actions.

What is important to apprehend, is that in the general sense, understanding follows from acting, it doesn't precede it, as we learn from experience. So theory follows practice. We find a practice which works, and we employ it, then we develop the theories to account for why it works. In this theoretical process, which is the "understanding" of the practice, it is of the utmost importance to determine the faults of the practice, exceptions, places where the practice produces less than perfect results. This is where proper understanding, and formulation of theory in a way which accounts for these discrepancies can lead to a better practice in the future.

So for example, the ancient practice of astronomy was to map the orbits of the planets as circles. This practice worked very well, and provided very good prediction, as Thales apparently predicted an eclipse. But there were slight imperfections. What was required was theoretical analysis of the slight imperfections, to produce a true understanding of the real orbits of the planets. That new theory produced a whole new set of practices which today extend far beyond the solar system. But the new practices have demonstrated their own imperfections. Therefore we need to revisit all the theory from bottom up to understand and account for these imperfections.

He's yet to answer the question I posed most likely because it isolates the underlying hypocracy of his debate stance -- apparently truth has little to do with his posting motivation -- so it's only pointless to argue against that which his hypocracy is productive of. His whole intellectual orientation is faulty. But it's for some reason been useful enough for him to maintain it.dex

To answer your question now, I believe it's a faulty goal to partake in this forum with the intent of persuading others. We are here as philosophers with the goal of understanding. We cannot treat each other as children to be persuaded, and even a minimal degree of participation will reveal that persuasion is never forthcoming. My goal in arguing the position I have argued in this thread is to bring to the attention of others, the slight imperfections which I've observed to exist within the practicing of mathematics. We can only move forward, collectively, by acknowledging, and accounting for these imperfections. To me, the imperfections are glaring, but every person perceives and apprehends things in one's own way. So some people cannot even see the imperfections, and others who see them dismiss them as being so minor that they're irrelevant (a difference which doesn't make a difference), so they end up denying that the imperfections are even imperfections. This is what I refer to as contradiction, to say that there is a difference which is not a difference, as the difference between ".999...", and "1".

The fundamental theorem of arithmetic states, in the modern reading, that all positive integers can be represented as a unique product of primes (barring order).

And what about 1? Is it excluded as a positive integer, or natural number? Or have you made the fractions into integers? Where does 1 fit in this theorem?

This is jargon... they refer to the same mathematical object.

That's simply an assertion. I have yet to see a definition of "mathematical object" which allows for the application of the law of identity. And the law of identity is what identifies an object as an object. To say that they refer to "the same mathematical object", says nothing more than that they are equal. And two distinct objects with the same value may be equal, and clearly not the same object according to the law of identity. So the phrase "they refer to the same mathematical object" is nothing but a deceptive use of jargon.

Sort of, but not really. "Number" applies to a lot of things. But that's not a problem; it's actually a benefit. The definition of number should not merely not be nailed down; it should be open. But part of the point of categorizing these numbers is so that we can give particular kinds of numbers names.

Sure, leaving the definition of "number" open is a "benefit"; to those who want to expand mathematical theory in any imaginable direction, like fishfry promotes, and also for those who argue by equivocation. For those who want to develop clear and consistent mathematical theory with universal applicability, it is detrimental.

Math is not subject to any standard of applicability. On the contrary, the only criterion for the worth of a piece of math is whether it's regarded as interesting and beautiful by mathematicians.

This is the fantasy that aesthetics is valued over and above good. It is a fantasy because we can only passively enjoy beauty for an extremely short period of time before our bodily needs get in the way and we are urged to act. The natural human condition is to act, so even the purest forms of theory are influenced by the urge to act.

MU has a metaphysical theory of numbers, he's a believer in them in the full b-word sense (it's part of his identity... almost literally), and modern math is kind of a heresy wrt it. That's my take. I personally envision his theories as being roughly of both the form and value of Eric the half a bee.

No. I don't seem to have a metaphysical theory of numbers, because I do not understand numbers well enough to create such a theory. What I do understand though, is that there is no metaphysical convention, and therefore no ontological coherency, in modern math. You might say that I believe in metaphysics, and modern math demonstrates a poverty of metaphysics.

I can't help being struck by the amount of mindshare Metaphysician Undercover holds here.

I would blame Banno, for declaring that this thread is about me. I'm just doing whatever I can to live up to Banno's expectations of me. See my respect for you Banno?

The result will be to show in even greater relief that this is a thread about Metaphysician Undercover, not about maths.
• 255
Good question. 1 is the product of zero primes: https://en.wikipedia.org/wiki/Empty_product
I have yet to see a definition of "mathematical object" which allows for the application of the law of identity.
Where have you looked? Or am I your personal search engine now?
Sure, leaving the definition
We have the terms rational and real, so, you're just whining.
I do not understand numbers well enough to create such a theory.
I'm still waiting for someone to explain to me how the so-called "object", or "number" which is represent by "1" and is by definition not a multitude, and therefore not composed of parts, can be divided into nine parts.
I note here that you're not just asking for a definition of number. You're asking for a definition of number that has these properties.

Also:
I'm a metaphysician, and some mathematical axioms are derived from metaphysical concepts such as the concepts of unity and continuity, which are features of "being", a subject of metaphysics. So I'm not exactly a layman on these issues.
• 29
That's just the problem, isn't it?! The ontological fallacy is that unity and continuity is what is real. But to get from the certitude which one is which required for logic to the certitude in the count of the duration between ends mathematics is requires a paradigm shift that has to be ignored or made to go unrecognized for there to be any metaphysics at all. It also means, in view pf current quantum and cosmological models, that space is contradictory, it returns to its origin by expanding in a straight line and yet has no center to the curve so described, and time resolves the contradiction by introducing opposing pairs of contraries that thwart the paradigm of unity and continuity that logic and math, and the metaphysics of "being", must convict itself in. This is what Plato shows us in his Laws, he spend hundreds of pages spoon feeding arithmetic order into the minds of the two saps accompanying him, only to recognize in the end that something irrational to that order, something deplorably human or personal, has to be admitted into the paradigm to even get it started, and to support any hopes it has of achieving unity and preserving continuity. that personal factor is not a complete overthrow of the paradigm, but a gradual nibbling away that changes it over time into what eventuates in something unrecognizable to its antecedents and yet never violating its criteria and modes of judgment. It does this, not by a revolutionary upheaval, but via personal characterizations of the conceit of unity in continuity we must always find ourselves convicted in. And this does not happen alone, it requires us to recognize in each other the incompleteness and misapprehension of the terms of our convictions. We become a community in contrariety that bends history towards justice, to paraphrase MLK.
• 4.6k
I partake in this forum to learn, and to help others learn.
So you teach that
Any system of interpretation which ignores the role of "+" within an equation, to claim that "2+2" says the same thing as "4", cannot really be taken seriously

Any system? And you wish to be taken seriously? And then there's the lie: what have you learned in this thread, for example?
• 7.2k
Good question. 1 is the product of zero primes: https://en.wikipedia.org/wiki/Empty_product

First class example of deception.

The ontological fallacy is that unity and continuity is what is real.

This is not necessarily a fallacy. It may be the case that the principles required to establish compatibility between the two, such that we can conceive of the two coexisting, as "what is real", have not been discovered.

Any system? And you wish to be taken seriously? And then there's the lie: what have you learned in this thread, for example?

If you think that you can explain the meaning of "2+2=4" by saying that "2+2", and "4" represent the same mathematical object, and "=" represents "is the same as", then I would say that you sorely misunderstand mathematics, and you ought not be taken seriously.

Do you understand that for an "equation" to be at all useful in honest mathematical practice, the right side must necessarily represent something different from the left side? If not, the equation would be a useless tautology. But that is how some people might present "2+2=4" as an example of a useless tautology in which "2+2" represents the very same thing as "4". But clearly that is not how equations are used by scientists and mathematicians. It is only how sophists who are attempting to persuade someone that "2+2" represents the same object as "4" might use an equation, and this is surely not honest mathematical practice.
• 937
That's not true

It is.
"the procedure proves what the procedure is supposed to", here, here, ...
Inconsistent. Recycle.

It becomes harder for @InPitzotl and @jorndoe to walk away the more they invest

You're right. Isn't the adventure into @Metaphysician Undercover's Wonderland oddly fascinating though? :) I guess it becomes trite after bit.

By the way, @Metaphysician Undercover, despite having been given references, you may of course ask for definitions of definitions of ... but I doubt anyone is going to teach you elementary school material on up. If you don't (or won't) get it, then so be it.
• 255
First class example of deception.
Yes, but it's quite ineffective... we already knew you weren't here to learn. Along the same lines, I never heard that paragraph after the one you quoted about the history of primes (gee, I wonder why, wink wink... o/c I know why and everyone with a browser can find out why in 30 seconds). Also along the same lines, that wiki page on mathematical objects that you could just as easily have looked up as the primes is still there.
• 7.2k
It is.
"the procedure proves what the procedure is supposed to", here, here, ...
Inconsistent. Recycle.

That the procedure produces an answer to the question, and the fact that the person uses the procedure to produce an answer, does not prove that numbers are objects. The procedure is designed to resolve a specific type of problem, not to prove that a number is an object.

Repetition: a person does not need to believe that a number is an object to carry out mathematical procedures.

Yes, but it's quite ineffective... we already knew you weren't here to learn.

You mean, I am here to learn, and not to be deceived, don't you? To fall for a deception which has been proven on others to be an effective deception, is not an instance of learning, even if the others believe it to be an instance of learning.
• 255
You mean, I am here to learn, and not to be deceived, don't you?
Alright I'll play. What is the nature of this deception?
• 642
What is important to apprehend, is that in the general sense, understanding follows from acting

Once apprehended, it should be incarcerated and prosecuted to the fullest extent. Understanding abets acting and is equally guilty.

You might say that I believe in metaphysics, and modern math demonstrates a poverty of metaphysics

Perhaps. But there are instances where it arises, like non-standard analysis which incorporates Leibniz's infinitesimals - which I claim are metaphysical actualities. And from my perspective, modern transfinite set theory seems somewhat metaphysical (others will probably disagree). The higher one goes into the thin air of mathematical abstraction the more likely one will encounter metaphysics - in my opinion. For example, one new developing area is that of "magnitude" in abstract spaces. Although the groundwork has been laid, this concept seems to me metaphysical. :cool:
• 7.2k
Alright I'll play. What is the nature of this deception?

The idea that one is a product of zero.

By "poverty of metaphysics", I mean poor metaphysics. And I consider infinitesimals as poor metaphysics, being a compromise between the incompatible principles of continuity and discrete units. So to me, it's like a monism which instead of respecting the reality of the two distinct and incompatible aspects of reality, which dualism recognizes, the metaphysics of infinitesimals blends the two together in an unintelligible vagueness where the two are assumed to be one.
• 7.2k
Sorry guys, but I know you all honestly believe in the true and real possibility of forever, but I'm a mere mortal, and cannot possibly entertain you all forever. So... Intermission!
• 255
The idea that one is a product of zero.
Oh you silly confused soul, seeing liars behind your eyelids. I suppose you also see lies in the fact that 3*3=9, given we're multiplying two threes and getting an odd number? Maybe this whole math thing isn't going to work for you.
• 642
And I consider infinitesimals as poor metaphysics

And I consider it the best of metaphysics, existing solely in the mind but useful in developing the mathematics describing physical phenomena.

Carson Chow (Scientific Clearing House, 2012):

But, then, I am not a philosopher and must bow to your competence in this area, as I have to your competence in mathematics. :cool:

(Refer to Metaphysics Defined in this forum)
• 937
Do you understand that for an "equation" to be at all useful in honest mathematical practice, the right side must necessarily represent something different from the left side? If not, the equation would be a useless tautology.

So you're not talking mathematics, or even logic for that matter, don't understand the formal expressions. (Which was observed earlier I guess.) Still going downhill. In a manner of speaking, proofs explicate tautologies.

prove that numbers are objects

Prove? Objects? The numbers are already operands in the procedures. There isn't anything to round off (you claim (that you believe)), but do it anyway. Inconsistent. What exactly are you rounding off if not 1/9 π √2 etc? Recycle.

I guess you don't believe in pocket calculators, which do not list kilograms, claws, or square miles, for example (cf mentioned invariance). You should at least understand what you're talking about before objecting and proclaiming (vast) conspiracies. :D References have been posted.

Sarcasm, ...? :)
• 8.9k
Do you understand that for an "equation" to be at all useful in honest mathematical practice, the right side must necessarily represent something different from the left side? If not, the equation would be a useless tautology.

If the left and right sides were different then they wouldn't be equal. What do you think the equals sign is?

You don't seem to understand the difference between expressions and values. $2+2$ and $4$ are different expressions with the same value. $9_{10}$ and $10_9$ are different expressions with the same value. $0.999...$ and $1$ are different expressions with the same value.

Or for a non-maths example, "water" and "H2O" are different expressions that refer to the same thing.
• 2.5k
The idea that one is a product of zero.

It’s not that one is a product of zero, it’s that one is the empty product.

Take any set of factors and multiply them together. Say for example {2, 2, 3, 5}. The product of those is 60, right? Now put a 1 in there, to make it {2, 2, 3, 5, 1}. Still 60 right? Put in another 1, and another, and another, and it doesn’t change anything right? Take away a 1, and another, and another, and it doesn’t change anything, right? Including or removing ones makes no difference to the product.

So if you have the product of {2, 2, 3, 5, 1, 1, 1}, and you get rid of the 5, then the product is 12 right? And if you get rid of a 1 it’s still 12. If you get rid of the 3 then the product becomes 4. If you get rid of a 2 then the product becomes 2. We’re down to {2, 1, 1} now if you’re having trouble following along.

Get rid of a 2 and the product becomes 1. Get rid of a 1 and the product doesn’t change — still 1. Get rid of another 1 and the product still doesn’t change. We’re down to the empty set here now, {}. That has the same product as {1} or {1,1} etc because including or removing 1s doesn’t make any difference.

If you put a zero into any of those sets, the product would become zero, yes; but we’re not doing that.
• 642
It’s not that one is a product of zero, it’s that one is the empty product.

"Multiplicative identity" is more appropriate. But whatever. It appears this thread will go to infinity without ever leaving the starting point. Paradox?
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