Prove it.However, we know that no matter how many 1s we put, even after we put an infinity of 1s (whatever that means), there would still be a remainder. — Metaphysician Undercover
The "unending 1s" indicates that there is a remainder — Metaphysician Undercover
P2. No matter how many 1s you write — Metaphysician Undercover
However, we know that no matter how many 1s we put, even after we put an infinity of 1s (whatever that means), there would still be a remainder. — Metaphysician Undercover
@Metaphysician Undercover <- look MU... free attention, freely given!With everything you're saying about numbers and division and the like, I honestly want to know what is going on in your head. — Michael
Prove it. — InPitzotl
You misunderstand — this is about the procedure, not about writing.
Go back, think about the procedure instead. — jorndoe
You misunderstand — this is about the procedure, not about writing.
Go back, think about the procedure instead.
In fact, we can go much further, though it requires some abstract thinking, e.g.: Repeating decimal (Wikipedia)
Hm regarding abstract thinking, in analogy: suppose we want to prove p; then by some other means we find that we can prove that p can be proven; well, then we're done with our initial task (unless we're curious). — jorndoe
We know that there isn't. I don't know why you think that you know more about maths than generations of professional mathematicians. With everything you're saying about numbers and division and the like, I honestly want to know what is going on in your head. Do you think that there's some grand conspiracy and they're lying to us? Do you think that you're an enlightened prodigy who is able to outsmart the people who have studied this stuff for years, despite probably having little to no formal training of your own? Seriously, I want to know. The psychology of this is fascinating. — Michael
I think the most important thing here is, what is MU's criteria for truth? MU made an actual truth claim here to counter a proof. Can MU offer a proof in return, or does MU think he has a better truth criteria? Either way, I want to see the proof or this better criteria. — InPitzotl
I don't think that I said I believe in the rationals. I was arguing using principles consistent with the rationals, so you inferred that I believe in the rationals. But arguing using principles which are consistent with one theory doesn't necessarily mean that the person believes in that theory. So I don't see your point here, I think you just misunderstood. — Metaphysician Undercover
What I argue against is inconsistency in the rules. And, if someone asked me to play chess, and I noticed inconsistencies in the rules, I would point them out. — MetaphysicianUndercover
I wonder what claim you think it being asserted by .999... = 1. — MetaphysicianUndercover
As I've demonstrated, we can still object to a specific set of mathematical rules, using a different set of mathematical rules to make that objection. — MetaphysicianUndercover
This is due to inconsistency in the rules of mathematics. Look at how many different systems of "numbers" there are. — MetaphysicianUndercover
I don't agree with this analogy at all. We apply mathematics toward understanding the world, and working with physical materials in the world. This is completely different from the game of chess. — MetaphysicianUndercover
If the principles of mathematics were not to some degree "true of the world", they would not be useful in the world. There is no such requirement in the game of chess. So it's completely acceptable to criticize the principles of mathematics when they are not "true of the world", because mathematics is used for purposes which require them to be true of the world. But the game of chess is not used in this way. So if I were to criticize the rules of the game of chess, it would be if I thought they were deficient for serving their purpose. — MetaphysicianUndercover
This is a nonsensical analogy. The rules of mathematics are used for a completely different purpose than the rules for chess. And the rules of math, to whatever degree they are not true of the world, lose there effectiveness at serving their purpose. The rules of chess are not used in that way. — MetaphysicianUndercover
Good... you're caught up then.But I don't see how expressing the remainder as a fraction resolves the issue of the remainder. — Metaphysician Undercover
Wrong. The fraction part of a mixed number specifies an exact portion of a unit. We can only say that 3/9=1/3 insofar as both of these fractions represent that specific quantity of a unit.The fraction is just an expression of an unresolved division problem.
Wrong. Assume I start with 24 pizzas. 2 rem 6 simply means that if I give each of 9 people just 2 pizzas, that I would have 6 left over.So in expressing "24÷9=2 rem 6", as 24÷9=2 6/9" or "2 2/3", all you are doing is replacing the remainder with an unsolved division problem. — Metaphysician Undercover
You didn't provide reasoning until just now; you just asserted it. Now let's go over your argument:It's been proven. It's called inductive reasoning. — Metaphysician Undercover
Correct. But also, every time someone adds another 1, is a time. Algorithmically, that time is a step; we can count the steps. Specifically, each step is a finite step. Might I remind you, though, that your truth claim is explicitly about "even after we put an infinity of 1s (whatever that means)"."'However, we know that no matter how many 1s we put, even after we put an infinity of 1s (whatever that means), there would still be a remainder.' — Metaphysician Undercover;
Prove it. — InPitzotl"
...Every time someone adds another 1, there is still a remainder. — Metaphysician Undercover
"never" applies to all steps in the process. And all steps are finite. So this does not apply "after" we put an infinity of 1s. (I would argue there's no such thing as that after).And never ever is there not a remainder.
We can conclude that for all steps. But we cannot conclude that "after" we put an infinity of 1s, which is the very thing you're making a truth claim about.And since the nature of the numbers stays the same, we can conclude that this will always occur.
I don't think that at some point we'll have enough 1s. I think you're once again speaking about something you have no clue about. There is no last finite counting number; there's no "point" "after" you have an infinite number of 1's. But there are an infinite number of counting numbers. I don't think you proved anything, except what you explicitly admitted to here... that you don't know what this means.I don't see what makes you think that at some point we'll have enough 1s that there'll suddenly be no remainder.
You're by context including infinite strings. The literal string .111... refers to an infinite string starting with .111 and followed by a 1 for every finite ordinal position; that is, if you count the first 1 as 1, the second as 2, and so on, there is no finite n such that the nth position does not have a 1 in it. There is no point in this string that is "the last 1" for the same reason there is no last counting number. Your argument hinges on the hidden assumption that there is such a step... but that's a confusion on your part.The criteria for truth is honesty. I provided my argument, and you disagreed with the second premise, that no matter how many 1s you place after the decimal point there will still be a remainder. — Metaphysician Undercover
Your honesty and sincerity is not in question; your claims are. Your proof falters because it does not apply to the one thing you're making a claim about. .111... is an infinite string; that is the thing under discussion. Your proof applies only to finite steps, which ipso facto is not infinite. By the way, because I use correct reasoning, I will not claim that your proof being wrong means there's no remainder; it does not mean that at all. What your proof being wrong means, instead, is that your reasoning that there is a remainder is invalid. I explicitly mention that because you make that mistake here:I think that this premise is true and I am honest in this claim. — Metaphysician Undercover
My honesty and sincerity is not in question; your claims are. Your proof still falters for the reason specified above.If you claim that you do not think that this premise is true, I think you are being dishonest. — Metaphysician Undercover
Wrong. Your claims stand or fall on their own merits; it has nothing to do with me. This isn't a relevant argument, it's a psychological response. You cannot conclude anything about the veracity of your claim based on presumed character flaws you guess I have.If that is the case, then your claim is false. — Metaphysician Undercover
I agree that just because you argue from certain premises doesn't mean you agree with them. But you are being disingenuous here. I could easily go back to our older discussions and show you where you accepted the rationals in order to deny 2–√2. I don't take this as a serious remark. Your prior posts don't support your claim that "I was only kidding about the rationals." You are retconning your posts and I'm not buying it. — fishfry
But that is fantastic! If you have discovered a specific inconsistency in the ZF axioms, you would be famous. Gödel showed that set theory can never prove its own consistency. To make progress we must either assume the consistency of ZF; or else, equivalently, posit the existence of a model of ZF. This by the way is what some readers may have heard of in passing as "large cardinals." For example there's a thing called an inaccessible cardinal. It can be defined by its properties, but it can't be shown to exist within ZF. If we assume that one exists, it would be a model for the axioms of ZF; showing that ZF is consistent. — fishfry
We do have exact definitions for natural numbers and integers, rationals, reals, complex numbers, quaternions, octonions, p-adic numbers, transfinite numbers, hypereal numbers, and probalby a lot more I don't even know about. But ironically, and confusing to many amateur philosophers, there is no general definition of number. A number is whatever mathematicians call a number. The history of math is an endles progressions of new things that at first we regard with suspicion, and then become accusotomed to calling numbers. — fishfry
You're not only a mathematical nihilist. You're a mathematical Philistine. "One who has no appreciation for the arts." You deny the art of mathematics. You know nothing of mathematics. — fishfry
You're just confusing pure and applied math. And missing the lessons of history that what is abstract nonsense in one era may well and often does become the fundamental engineering technology of a future time.
You know when Hamilton discovered quaternions, nobody had any use for them at all. Today they're used by video game deveopers to do rotations in 3-space. Did you know that? Are you pretending to be ignorant of all of this? That when you run the world nobody will do any math that isn't useful today? — fishfry
I don't see your point. — Metaphysician Undercover
I've seen some mathematical proofs, and as I've shown that the axioms are full of inconsistencies and contradictions. A lot of these so-called "proofs" are smoke and mirrors built on false premises and therefore unsound. — Metaphysician Undercover
The fraction part of a mixed number specifies an exact portion of a unit. — InPitzotl
By contrast, the fraction specifies an exact quantity. It means a specific thing to give one person 2 2/3 pizzas. If I give each of 9 people 2 2/3 pizzas, then I have none remaining. — InPitzotl
never" applies to all steps in the process. And all steps are finite. So this does not apply "after" we put an infinity of 1s. (I would argue there's no such thing as that after). — InPitzotl
We can conclude that for all steps. But we cannot conclude that "after" we put an infinity of 1s, which is the very thing you're making a truth claim about. — InPitzotl
I don't think that at some point we'll have enough 1s. — InPitzotl
The literal string .111... refers to an infinite string starting with .111 and followed by a 1 for every finite ordinal position; that is, if you count the first 1 as 1, the second as 2, and so on, there is no finite n such that the nth position does not have a 1 in it. — InPitzotl
Your proof falters because it does not apply to the one thing you're making a claim about. .111... is an infinite string; that is the thing under discussion. — InPitzotl
What your proof being wrong means, instead, is that your reasoning that there is a remainder is invalid. — InPitzotl
It would seem so. Your comments are still off topic.
Back to the topic here:
We can prove that all the procedure does here is give us 0, decimal point, followed by endless 1s.
And we can prove that without writing down 0, decimal point, followed by endless 1s — it's an artefact of the procedure, and the proof involves mathematical induction and such.
Doesn't really matter much whatever anyone makes of it, that's how the arithmetic works.
That was the topic brough up, though we can prove more than just that (repetend length is 1).
But, proof or not, this should be intuitively clear. You understand? If yes, then you're free to suggest a means to communicate this unambiguously, or you can follow typical conventions like 0.1¯=0.(1)=0.111…0.1¯=0.(1)=0.111…. — jorndoe
You didn't really answer the question though. Do you believe that generations of mathematicians are aware of this, and yet for some reason continue to use them, or are they unaware, and you're just smarter than everyone else? — Michael
I don't think you can cast a net of generality on all mathematicians in that way. Some follow the discipline in such a way that they would apply the principles without being aware of the underlying issues. Fishfry might call this applied math. Some question the underlying principles, as indicated by jgill. Fishfry might call this pure math. If I understand fishfry's proposed divisions.
Furthermore, there are multitudes of complex problems involved with what might be called "pure math". If there is such a thing as "pure math" it would involve analyzing these problems. And those who are interested in addressing the problems direct their attentions toward the issues which interest them. For instance, jgill suggested I direct my attention toward the axiom of choice, but it's not my interest right now.
So there's no issue of anyone being smarter than anyone else, I don't know how you would even judge such a thing. It's a matter of where one's attention is directed. I happen to have an interest in music, and musicians work with a fundamental unit called an octave, along with divisions and multiplications, using frequencies to produce harmonies and dissonance. So the matter of what can and cannot be divided into equal parts is interesting to me. The issue of the acceptable divisions of a unit has never been resolved. And to claim as InPizotl seems to, that a unit can be divided in any way one pleases is totally unrealistic. However, notice that my interest in the problems of division is piqued by my interest in music, such that the pure side of my math interest is still guided by the applied side. And this is why I do not accept fishfry's proposed division. — Metaphysician Undercover
Hmm... No pattern recognition...? Odd.I'm sure my intuition is quite different from yours — Metaphysician Undercover
Nope. Arithmetic works fine regardless of notational conventions.Doesn't the second statement directly imply the falsity of the first? — Metaphysician Undercover
We can prove things about switching 1/9 to decimal form without doing it (↑ stands on its own).We can prove that all the procedure does here is give us 0, decimal point, followed by endless 1s.
And we can prove that without writing down 0, decimal point, followed by endless 1s — it's an artefact of the procedure, and the proof involves mathematical induction and such.
Doesn't really matter much whatever anyone makes of it, that's how the arithmetic works.
We've been through this MU. We're not debating... you're under the delusion that we're having a debate... that my goal is to persuade you, that I'm trying to do so, that something is riding on your agreement, and that it actually matters that I persuade you. We're not, I'm not, I'm not, it isn't, and it doesn't. But I have to say... it's all kinds of adorable that you think we're debating!reasserting it will not persuade me to agree. — Metaphysician Undercover
The fact that there is a repeating decimal — Metaphysician Undercover
The decimal is a red herring; 2/3 is a fraction, not a decimal point number. You're conflating notation with representation.Therefore it is impossible that 2/3 represents an exact portion of a unit. — Metaphysician Undercover
But I can. I can use a pizza cutter, I can slice a pizza into 3 equivalent parts, and then I have thirds of a slice.What you have argued is that you can define "one" or "unit" however you please — Metaphysician Undercover
It's no contradiction; we just specify the units. I slice 6 of the pizzas into three slices each. Now I have 18 pizzas and 18 thirds-of-pizzas. I give each of 9 people 2 pizzas and 2 thirds-of-a-pizza. This is something I can actually do in real life. Keeping track of two kinds of things (pizzas, slices-of-pizza) is child's play. If you have difficulties doing that, that's your problem not mine.and that's just contradiction plain and simple. — Metaphysician Undercover
Well likewise no offense intended MU on my part but, I can't possibly take any of your arguments seriously, including your ad hominem conspiracy theories about me. So there's no way you offend me by this... all you're managing to accomplish is to expose your own irrationality.You're intentionally avoiding the point, and I must say, lying, when ... Sorry, no offence meant, but I feel it's necessary to point this out. — Metaphysician Undercover
That is literally untrue. I have a BS minor in math; I'm pretty sure that qualification covers mixed numbers, since that's a grammar school topic.You have no qualifications here — Metaphysician Undercover
...is exactly as relevant when talking about thirds as it is when talking about wholes. Now that I described what that process is, let's compare notes. There is a real thing I can do to distribute 24 pizzas among 9 people (above). Your objections fail to describe or affect that procedure; worse, they fail miserably to account for the fact that I wind up with no pizzas instead of six.to stipulate the size of the pizza
There's no disagreement about finite decimals, but it's irrelevant to 0.111....Actually my truth claim was that — Metaphysician Undercover
There is no "then" here... belief is not a mandate. You cannot defend a false belief on the basis that nobody offered you an alternative...Now, can you give me an honest answer to how you think the remainder is dealt with then, — Metaphysician Undercover
There's nothing special about the decimal system with respect to number values. 1/9 is 0.01_{3} exactly, no remainder. 1/9 as a fraction is a value in and of itself. The question under concern is whether 1/9 can be represented exactly by the decimal system. It can, if your decimal system includes (or is extended to include) repeated decimals, and if you use the definition I supplied earlier for repeated decimals. The OP provided a proof of this.such that we can end up with an "exact quantity".
Oh, thank you MU. It saves a lot of time when you make a claim but accidentally prove by contradiction that it's false (underlined). If you can describe this string as "an infinite string" and reason about what that implies, then I can refer to the same string as "0.111..." and reason about what that implies. As a bonus points, you've demonstrated that you yourself are just confused about this, which is something I keep saying.No, .111... cannot refer to an infinite string, because we've agree that we cannot put an infinite string there. — Metaphysician Undercover
No, you're confused. I'm claiming to do what you (accidentally) proved by demonstration is possible.You are now claiming to do what we've agreed is impossible. — Metaphysician Undercover
That's easy. "We cannot put an infinite string there" is a true statement.Which do you accept as the truth, can we put an infinite string there or not? — Metaphysician Undercover
Silly MU. I only claim that "..." refers to an infinite string. Call it 0.(1) if that helps. It all refers to the same idea... that the program generating this string never halts and always repeats as demonstrated by symmetric recursion.If you say that .111... refers to an infinite string that is somewhere else other than there, — Metaphysician Undercover
It's trivially relevant, because it's the infinite string referred to by "0.111..." that you are trying to object to.then how is it relevant?
(a) yes, the program never halts. (b) Not really; we use "0.111..." to refer to the fact that it never halts (and that all of the symbols in it are 1's). I got to this from the program by running just a few steps, and recognizing symmetric recursion was going on. (c) No, we used reason to conclude (a) and (b) and call this an infinite string of 1's. And I'll add (d), that your proof only applies to terminating decimals, because we can only say that a result has a remainder if we're "left" with one "after" we're done, and there's only such a thing as "done" for terminating decimals.You've refuted my proof by proposing that (a) there cannot be an "after" one (b) puts an infinity of 1's there, and then (c) going and putting an infinity of 1's there. — Metaphysician Undercover
If there's no after putting an infinity of 1's, there's no such thing as the remainder you're left with when you do. To talk about such an entity you have to either reify it, or prove it actually exists. Good luck talking about the remainder at the final execution step just prior to halting, in the context of a program that never halts.Now we are at the point of after you put the infinity of 1's there, — Metaphysician Undercover
You have this backwards. I don't have to prove your proof doesn't prove something, your proof has to prove it. We have an object 0.111... that describes the output of a program that never halts. You applied fallacious reasoning akin to my previously mentioned troll proof that infinity is finite; "it has a remainder at each step, therefore the infinite string has a remainder" is exactly analogous to "it's finite at each step, therefore infinity is finite". We trivially know this doesn't apply, because there is no such thing as a last step to have a remainder at. There is no counting number that represents the count of the counting numbers. There's no "after" to writing an infinite number of 1's. There's no "end" to a program that never halts.so all you have done is disproven the premise of your refutation.
This doesn't answer my question. Do you think that mathematicians are aware that "the axioms are full of inconsistencies and contradictions. A lot of these so-called 'proofs' are smoke and mirrors built on false premises and therefore unsound"? — Michael
If they are then why do they use them and not "fix" them? — Michael
If they're not then how are you, a mathematical layman, able to notice what the experts can't? — Michael
We can prove things about switching 1/9 to decimal form without doing it (↑ stands on its own).
You understand...? — jorndoe
If yes, then you're free to suggest a means to communicate this unambiguously, or you can follow typical conventions like 0.1¯=0.(1)=0.111…0.1¯=0.(1)=0.111…. — jorndoe
We've been through this MU. We're not debating... you're under the delusion that we're having a debate... that my goal is to persuade you, that I'm trying to do so, that something is riding on your agreement, and that it actually matters that I persuade you. We're not, I'm not, I'm not, it isn't, and it doesn't. But I have to say... it's all kinds of adorable that you think we're debating! — InPitzotl
But I can. I can use a pizza cutter, I can slice a pizza into 3 equivalent parts, and then I have thirds of a slice. — InPitzotl
There is a real thing I can do to distribute 24 pizzas among 9 people (above). Your objections fail to describe or affect that procedure; worse, they fail miserably to account for the fact that I wind up with no pizzas instead of six. — InPitzotl
The second run is qualitatively different, but we can still represent what it does. We know that there's no complete output of this program because we know it will never halt; but we know the program keeps generating 1's in perpetuity. We know we cannot write down the full output here, because we know it is infinite, but we know that its output will keep spitting 1's because it did so for a couple of steps and because the nature of the infinite loop is that of symmetric recursion. So we can represent the output as 0.111... meaning it never stops, and will always spit out 1's. "An infinity of 1's" is just a shortcut for saying the same thing. "One repeating" says the same thing as well; 0.(1) refers to the same thing. — InPitzotl
Oh, thank you MU. It saves a lot of time when you make a claim but accidentally prove by contradiction that it's false (underlined). If you can describe this string as "an infinite string" and reason about what that implies, then I can refer to the same string as "0.111..." and reason about what that implies. As a bonus points, you've demonstrated that you yourself are just confused about this, which is something I keep saying. — InPitzotl
There's no "end" to a program that never halts. — InPitzotl
The prime commandment is that One must be kept whole. At the alter he sacrifices all of mathematics beyond addition. — Banno
You know that the value of "one" is that of a whole, a single unit, do you not? If it is divided in half for example, then the two halves together can not have an equal value to the "one" which is a single, not a double. If there is such a thing as "pure mathematics", then the unit which is represented by "1", being simple, must be distinct from the unit represent by "2", or "3", being multiplicities. The need to divide the fundamental unit "1" is a feature of application. Only in reference to the particulars of the application can the divisibility of that which is represented by "1" be determined. In other words, the divisibility of "1" is dependent on, and determined by the divisibility of the object which it is applied to in application. — Metaphysician Undercover
...a four-year-old girl may be shown a picture of eight dogs and three cats. The girl knows what cats and dogs are, and she is aware that they are both animals. However, when asked, "Are there more dogs or animals?" she is likely to answer "more dogs". This is due to her difficulty focusing on the two subclasses and the larger class all at the same time.
Multiple things. Playing a game. I'm trying to see how much perspective I can give you about your lack of competence in this area... that you're uncooperative makes it a bit challenging. But I'm being quite honest here; I don't take you seriously.What are you doing then? — Metaphysician Undercover
Well seeing as the pizzas themselves wouldn't be exactly equal either, why would we care? It doesn't affect the definition of fractions, and 9 people are getting more pizza than they would if you threw 6 in the trash. I'm pretty sure 6 pizzas in the bin because you have some sort of deep rooted aversion to fractions is more significant mathematically speaking than guy 3 getting a few tenths of an ounce more pizza than guy 4 because we're approximating fractions (not to mention hand waving that whole pizzas weigh the same, for some mysterious reason).And what do you say when we weigh the slices and find out that they are not exactly equal? — Metaphysician Undercover
Your criteria for failure amuses me. I have 9 happy people. You have 6 pizzas in the trash.Sorry, but your example is what fails miserably. — Metaphysician Undercover
Don't I?You seem to misunderstand. — Metaphysician Undercover
What I'm arguing is that an infinite string of 1's. following a decimal point, following a zero, does not represent a solution to one divided by nine.
But you failed to prove there's still a remainder in an infinite string of 1's following a decimal point following a zero.Sure, but as I said, there's still a remainder — Metaphysician Undercover
Without an end, when do you have a remainder? (Did you not see where I pointed out the flaw in using your argument to show there was a remainder? That's "Proof" A, it's still in the post, countered by "Proof" B, and satirized by "Proof" C).Exactly! Without an end the problem is not resolved. — Metaphysician Undercover
I'm doing multiple things at once; debating just isn't one of them. I'm trying to see, as a challenge, how much perspective of math community you will take in while being paranoid about it. I'm attempting to reverse engineering your jaded views of the math community.And, as you say we are not debating this, nor are you trying to persuade me of your point of view, so why continue? — Metaphysician Undercover
Yes; I'm learning about how you think.Are you learning anything yet? — Metaphysician Undercover
If we're talking about integers, sure. If we're talking about fields, no. It's intriguing to me that you take this sort of integral and/or whole and/or counting number realism to such extreme deepisms that you both transport the properties of such things into other number systems and trick yourself into thinking you've done something profound, but I have no actual interest in the broken theories that lead to this. I am however interested in the psychological aspects of why you're so committed to these deepisms... but not being a psychologist I'm content with just what I can piece together with reverse engineering.Would you consider the proposition that certain numbers just cannot be divided by each other? — Metaphysician Undercover
If pure math can have no fractions, what is this?:You know that the value of "one" is that of a whole, a single unit,... — Metaphysician Undercover
I'm learning about how you think. — InPitzotl
"two rows containing equal numbers of blocks are placed in front of a child, one row spread farther apart than the other, the child will think that the row spread farther contains more blocks". Pushing the block together seems to the child to decrease the number of blocks. — Banno
Most folk can manipulate "one" in quite complicated ways. They learn to speak of one dozen, for example, understanding that they can treat twelve things as if they were an individual. They can have half a glass of water without having an existential fit about the non-existent other half. — Banno
Talking to you has similarities to talking to a pre-operational child. — Banno
Multiple things. Playing a game. I'm trying to see how much perspective I can give you about your lack of competence in this area... that you're uncooperative makes it a bit challenging. But I'm being quite honest here; I don't take you seriously. — InPitzotl
Well seeing as the pizzas themselves wouldn't be exactly equal either, why would we care? — InPitzotl
But you failed to prove there's still a remainder in an infinite string of 1's following a decimal point following a zero. — InPitzotl
Without an end, when do you have a remainder? — InPitzotl
If we're talking about integers, sure. If we're talking about fields, no. It's intriguing to me that you take this sort of integral and/or whole and/or counting number realism to such extreme deepisms that you both transport the properties of such things into other number systems and trick yourself into thinking you've done something profound, but I have no actual interest in the broken theories that lead to this. I am however interested in the psychological aspects of why you're so committed to these deepisms... but not being a psychologist I'm content with just what I can piece together with reverse engineering. — InPitzotl
1. the arithmetic procedure gives 0 decimalpoint and endless 1s (provable by, say, mathematical induction, reductio, whatever) — jorndoe
Some are, some aren't. — Metaphysician Undercover
Some are actively trying to fix them. There's not universal acceptance of all mathematical axiom because some mathematicians propose alternatives. They are trying to fix the problems. — Metaphysician Undercover
Wrong. To persuade is to convince someone that something is true. You are, in my estimation, unpersuadeable; you've invested huge chunks of your time developing your weird theories and creating narratives to rehearse... your own personal thought terminating cliches (I've seen them), and you're not going to give that up. To see a perspective is entirely different; that is simply to understand what another's view is. As I've said multiple times, I could care less whether you believe the math or not. The only thing I'm giving a shot at is for you to see how the math works.In other words, you're trying to persuade me. — Metaphysician Undercover
Quite the contrary... it's the epitome of utility. Each of 9 people are getting dramatically closer to an equal portion of the 24 pizzas with this method than they are with 6 pizzas in the bin.This is why the example, as proposed, is not useful. — Metaphysician Undercover
Wrong. You are dealing with integers or some subset thereof, arbitrarily calling that numbers, ignoring the concepts laid out before you while making deepist excuses and deluding yourself into thinking that by doing so you've actually made some sort of interesting fundamental point.We are dealing with numbers, not with pizzas, and discussing the basis (principles) upon which we divide quantitative values. — Metaphysician Undercover
There's nothing to make clear to me; this is illusory insight. The examples demonstrate that there is another concept here. Along with those six pizzas with not-quite-equal slices going into the bin you're chunking out perfectly valid mathematical ideal slices of ideal equal weight into the bin, with excuses. The excuses give you the illusion that you're being rational, but they are irrelevant with respect to throwing away the principles of rationals. They are, however, relevant to what mathematicians talk about.I've tried to make this clear to you, but you keep going back to these examples. We are dealing with numbers, not with pizzas, and discussing the basis (principles) upon which we divide quantitative values. — Metaphysician Undercover
But you have an illusory insight with no valid truth criteria. You're in essence making an idol of integers, arbitrarily calling that number, and pretending you've done something fundamental.As soon as we come to a mutual agreement about the divisibility of quantitative values (abstract numbers) — Metaphysician Undercover
The problem isn't that I refused it. The problem is that it didn't prove what you claimed it proved.I gave you an inductive proof and you refused it. — Metaphysician Undercover
Try this... instead of 1/9, let's do 1/7. Now our description has to change, because we get 0.(142867). So yes, each "time" the machine is forced to "loop back" it's because there's a remainder. But what is the remainder to 0.(142867)? Is it 3, 2, 6, 4, 5, or 1? Note that "each time the machine is forced to 'loop back'" it is because there is exactly one of these left as a remainder. Is there exactly one of those left as a remainder to 0.(142867)? Can you even answer these questions... do they have an answer? I'll await your reply before commenting further.Each time the machine is forced to "loop back" it is because there is a remainder which must still be divided. — Metaphysician Undercover
No, we're not. No mathematician denies that division is not closed in the integers; if you look back, you'll see where I actually posted the same thing in a prior post. You're denying that we can divide at all, and field division by definition can do so. The real discussion then is whether we're doing integral division using decimals or rational division, and since decimals are driven by powers of tens (including powers of tenths), it's immediately apparent it's rational division. But because you worship the idol of the integers, you're incapable of using the appropriate language for the appropriate context.Good, we're making some progress toward principles of agreement. — Metaphysician Undercover
You've got it backwards. They're derived from the axioms of the system you're using. The axioms define various relationships between undefined terms. The application demands use of an appropriate axiomatic system whereby the mappings of the undefined terms have the relationships described by the axioms.If you recognize that there are some restriction which may apply to the division of a unit, due to the nature of the unit, then you ought to understand that the conditions are derived from the real particulars of the application. — Metaphysician Undercover
Because we define it. Incidentally in terms of application we can use this in arbitrarily complex ways. There are some 10^{80} atoms in the universe, but we can practically get far smaller than 10^{-80} by applying arithmetic coding to text. Note also that machines can far exceed what we can do, so the limits of what we can do are not bound by some smallest unit of some extant thing... they're bound by the furthest reaches of utility we can possibly get from machines. We can get much further not limiting our theories in silly inconsistent ways. But even without all of this, just for the math is all of the required justification.Why would you think that there is any type of thing, like a field or whatever, which would admit to any possible division imagined, whatsoever? — Metaphysician Undercover
This is what I disagree with. Instead, I think that one divided by nine is an impossible procedure, provable by induction. — Metaphysician Undercover
I thought all mathematics is addition, with just some techniques for doing it efficiently. — tim wood
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