I didn't say any did. I imagine some have, or maybe not. That's not relevant because it doesn't mean that it's wrong for me to. — Metaphysician Undercover
What I mean is something like this:Well, if you think that I haven't already seen how math works, then you're wrong. — Metaphysician Undercover
I haven't seen that definition. — Metaphysician Undercover
I have no idea what you're talking about — Metaphysician Undercover
...I've never seen any such definition of "division — Metaphysician Undercover
I've made from what I've seen is that a healthy dose of skepticism — Metaphysician Undercover
...no; blaming the mathematicians for your not finding the remainder is not healthy skepticism.I can't see how this makes any relevant point. You've just demonstrated another smoke and mirrors method to hide the fact that there is a remainder. — Metaphysician Undercover
You didn't answer the question, and I think the reason you didn't is because the question doesn't make sense. That carries over to your previous claim that 0.111... has a remainder.Where's the problem? — Metaphysician Undercover
...so... 0.(1)=1/9?I don't deny any of this, that's how math works, conventions are followed, and that's what convention has us call "dividing". — Metaphysician Undercover
Logical deduction based on the axioms.The question is on what principles do we say that the conventions are right or wrong. — Metaphysician Undercover
Sure, why not? Something like: 97*104=97+(100-3)(100+3)=97+10000-9=10088?Do you agree that for any particular way that an action is carried out (an action being the means to an end), in this case a mathematical operation, it is possible that there might be a better way? So even if — Metaphysician Undercover
That's quite a fair description of Finite Geometry.You seem to think that mathematics works because people dream up random axioms, then the axioms are applied, and voila, mathematics works. — Metaphysician Undercover
No it doesn't:I start with the fundamental principle of "pure mathematics", which states that — Metaphysician Undercover
Part of the reason I post this definition (and rearrange this) is context for the response below:Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. — Pure mathematics (wikipedia)
Examples of pure mathematics becoming useful (exact opposite of what you just said) here.I think that mathematics works because people design the axioms so as to be applicable to the real world. — Metaphysician Undercover
I start (frontwards) with the axioms.You start with the opposite (and what I claim backwards) position, that the fundamental "unit" is divisible any way one can imagine, an infinity of different ways. — Metaphysician Undercover
I wouldn't go that far... it's just useful.First, I will argue that this annihilates pure mathematics — Metaphysician Undercover
Interesting... you claim that I've demonstrated that I believe any object can be divided an infinity of ways, and yet, in the same post, you quote me as saying there's about 1080 atoms in the universe. Ladies and gentlemen... MU's healthy skepticism!Second, I will argue that it leads you to believe, as you've demonstrated in this thread, that any object is divisible in any way imaginable, i.e. an infinity of different ways. — Metaphysician Undercover
No clue what you mean by that, so I'll just generically offer that arithmetic encoding works based on the same concepts we're discussing here... converting fractions (representing ranges of relative symbol frequencies) into placement systems (representing the coding).This demonstrates my point. — Metaphysician Undercover
Here's the problem. — Banno
So it's just you against the world of mathematics. If that can't convince you that your views are the problem, not mathematics, then I don't think anything will. — Michael
..no; blaming the mathematicians for your not finding the remainder is not healthy skepticism.
Where's the problem?
— Metaphysician Undercover
You didn't answer the question, and I think the reason you didn't is because the question doesn't make sense. That carries over to your previous claim that 0.111... has a remainder. — InPitzotl
No it doesn't:
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications.
— Pure mathematics (wikipedia)
Part of the reason I post this definition (and rearrange this) is context for the response below:
I think that mathematics works because people design the axioms so as to be applicable to the real world.
— Metaphysician Undercover
Examples of pure mathematics becoming useful (exact opposite of what you just said) here. — InPitzotl
No it doesn't: — InPitzotl
Interesting... you claim that I've demonstrated that I believe any object can be divided an infinity of ways, and yet, in the same post, you quote me as saying there's about 1080 atoms in the universe. Ladies and gentlemen... MU's healthy skepticism! — InPitzotl
I told Banno already in this thread, I do not believe in mob rule. I'm an individual, and what makes an individual an individual, is to not be identified as a part of a group. Therefore it's natural that I be different from the others. This is what makes "one" fundamentally different from "half of two". The former identifies the thing being spoken about as an individual, the latter identifies the thing being spoken about as a member of a group. The mistake which many people partaking in this thread make, is that they think that because "one" is equal to "half of two", in mathematical applications, they both mean the same thing. But I believe myself to be "one", an individual, and my identity is not based in being a member of that group. Therefore I need not partake in their mistake. — Metaphysician Undercover
You seem to always misunderstand, or misrepresent what I say. I didn't ever blame the mathematicians for "not finding the remainder", I blamed then for hiding the fact that there is a remainder. And this is clearly evident from what is expressed in the op, when it is asserted that the follow is an accurate representation: 1/9=.111..., and .111...X9=1. And, I suggested that mathematicians ought to respect the fact that it is impossible to divide one by nine equally, instead of using smoke and mirrors tactics to make it appear like this impossible thing is possible. To me, it just makes the mathematicians look bad, more like mathemagicians. — Metaphysician Undercover
I told Banno already in this thread, I do not believe in mob rule. I'm an individual, and what makes an individual an individual, is to not be identified as a part of a group. Therefore it's natural that I be different from the others. This is what makes "one" fundamentally different from "half of two". The former identifies the thing being spoken about as an individual, the latter identifies the thing being spoken about as a member of a group. The mistake which many people partaking in this thread make, is that they think that because "one" is equal to "half of two", in mathematical applications, they both mean the same thing. But I believe myself to be "one", an individual, and my identity is not based in being a member of that group. Therefore I need not partake in their mistake. — Metaphysician Undercover
Mathematicians aren't making mistakes. 1/9 is a number and 0.999...=1. If you don't understand this then you don't understand mathematics. I suggest you study more before wildly claiming that mathematics is contradictory and derived from false premises. — Michael
So, the answer to the question of what the remainder of 0.(142857) is, is that there is in fact a remainder, it's clearly evident, mathematicians ought to respect that it is impossible to divide one by seven, and mathematicians are using smoke and mirrors to hide the fact that there is a remainder?I didn't ever blame the mathematicians for "not finding the remainder", I blamed then for hiding the fact that there is a remainder. — Metaphysician Undercover
You're ignoring a key part of your Wikipedia definition: "may", not to mention the bolded part.You're ignoring a key part of your Wikipedia definition, "These concepts may originate in real world concerns...". — Metaphysician Undercover
Multiple examples provided in link of utility following math.... then to simply assert "no it's doesn't" is completely insufficient. — Metaphysician Undercover
Of course. But the object represented as 1 is a mathematical object, not an onion. Nobody is claiming you can chop an onion into infinite pieces. But we can subdivide 1 indefinitely; there's no "math-atom" we run into. We can apply arithmetic coding for example to encode 10G of text, which means we can generate an arbitrary precision number with on the order of ten's of G's of symbols. So it turns out, you're the one confused, not me; you think 1 is a pizza or an onion. It's not. It's a number.An object, represented as "1", can be divided in an infinity of different ways. — Metaphysician Undercover
Mathematicians aren't making mistakes. 1919 is a number and 0.999...=10.999...=1. If you don't understand this then you don't understand mathematics. I suggest you study more before wildly claim that mathematics is contradictory and derived from false premises. — Michael
1919 in base 10 is equal to 110110 in base 9, so 0.111...0.111... in base 10 is equal to 0.10.1 in base 9. It's divided equally. — Michael
Of course. But the object represented as 1 is a mathematical object, not an onion. Nobody is claiming you can chop an onion into infinite pieces. — InPitzotl
Great, now we're making some progress — Metaphysician Undercover
we are talking about dividing the number represented by "1", not some physical object... how do you propose that it might be divided. You cannot take a knife or a pizza roller to it. — Metaphysician Undercover
It is the case that you do not understand.It's not the case that I don't understand — Metaphysician Undercover
By just doing so. I gave you an example, which is quite relevant, to help you understand. You ignored it. But it's still there. If you're going to ignore what I say, I'm not going to pretend we're having a conversation.how do you propose that it might be divided. — Metaphysician Undercover
...then you need to understand that example.So I really want to know what principles you are applying to divide 1 — Metaphysician Undercover
I don't see that your making a point. Base 9 is going to have its own numbers which are impossible to divide into each other. So this just emphasizes my point, what can and cannot be divided is dependent on the application. — Metaphysician Undercover
Great, now we're making some progress. You see that your pizza analogy is completely irrelevant, and we are talking about dividing the number represented by "1", not some physical object. Is the number represent by "1" a single unit or a multiplicity of units? Since it is not a multiplicity, as it is defined as a single, then how do you propose that it might be divided. You cannot take a knife or a pizza roller to it. What do you think, that you can imagine that it's really made of parts, a multiplicity, and you can divide it according to those parts? Of course that image would contradict the definition. So I really want to know what principles you are applying to divide 1, because you seem so insistent that you can divide it however you please. — Metaphysician Undercover
By just doing so. I gave you an example, which is quite relevant, to help you understand. You ignored it. But it's still there. If you're going to ignore what I say, I'm not going to pretend we're having a conversation. — InPitzotl
If we can talk about dividing a single cake into nine equal slices then we can talk about each slice being one-ninth of a cake, and if we can talk about each slice being one-ninth of a cake then we can talk about 19 — Michael
Where the problem is, is in what fishfry called pure math, which is when we are working solely with abstract concepts. In abstract math the thing being divided into nine parts is the "number" one, or the "unit" one, and this division is said to give a "number" with the value of "0.111...". This is where I see a problem , as I've tried to explain. — Metaphysician Undercover
I can't say that I completely understand your representation so I can't give an honest answer here. Perhaps you could explain better. — Metaphysician Undercover
Yeah sure, that's fine — Metaphysician Undercover
So we can't divide a pizza into 9 slices because the slices don't weigh the same, and we can't divide 1 into 9 because 9 isn't infinity.It doesn't answer my question, and it's false. First, my question concerns the principle by which you divide a number, not the act by which you represent this, which is what your example describes. Second, your example is false and invalid because "ten's of G's of symbols" is not the same as infinite. — Metaphysician Undercover
The problem is in dividing "1". — Metaphysician Undercover
Of course. But the object represented as 1 is a mathematical object, not an onion. — InPitzotl
Or, we could skip all that and just start at base two. Can you show me how to divide 1 in binary? — Metaphysician Undercover
The problem is in the supposed equivalence between the fraction and decimal representation. Do you understand, that by moving to base nine, you are actually removing the possibility of dividing one by nine, because nine has been excluded as a number? — Metaphysician Undercover
Oh that's rich.You're just distracting from the topic. — Metaphysician Undercover
^^ 1/9 is that thing.my question concerns the principle by which you divide a number — Metaphysician Undercover
^^ distraction.is not the same as infinite. — Metaphysician Undercover
Meta has revealed that one cannot subtract from a whole. Subtraction only works if you have more than one individual. And division leads to the heresy of fractions. — Banno
There is no such thing as one half, unless it is a half ofsomethingwhatever/anything (hence an abstract quantity) — Metaphysician Undercover
... doesn't seem right. You can be both honest and wrong.The criteria for truth is honesty. — Metaphysician Undercover
Your replies are vague and hard for me to understand. That the procedure proves what the procedure is supposed to prove is not the issue. — Metaphysician Undercover
:D We're no longer talking mathematics. — jorndoe
This is equivalent to
12=0.512=0.5 in base 10. — Michael
Nine hasn't been excluded as a number. There are nine apples in the picture above regardless of what base you use to count them. This is exactly what I mean by saying that you don't understand maths. — Michael
Despite what you seem to be a saying, a number doesn't have to be representable as a terminating base 10 decimal. There are an infinite number of numbers that can't be represented this way. Some can be represented as terminating decimals in other bases. Others can't be represented as a terminating decimal in any base. And they're all still numbers. — Michael
You can be both honest and wrong. — jorndoe
Mentioned procedure just writes 1/9 as 0.111... (in the common decimals). — jorndoe
This is not true at all. If 1 is divisible, its divisibility is different in base nine from what it is in base ten. That's why I asked you to look at base two as an example, because it becomes very clear there, that if one is divisible, changing the base changes the divisibility of one. Therefore, if fractions are numbers we cannot transpose these numerical values from one base to another in the way that you propose. — Metaphysician Undercover
Due to the fact that what can and cannot be represented is dependent on the mode of representation, this claim employs equivocation in the term "numbers". This is the reason why we use different numbering systems, natural, rational, real, for example, and that "number" has a different meaning in each of these systems, just like the base unit "one" has a different meaning in each base system, if "one" is divisible. To claim that "they're all still numbers" is just a matter of equivocation, similar to saying that all uses of "right" refer to the same type of thing a right, unless you can demonstrate a definition, or category of "number", which encompasses all the different numerical systems. Under this definition of "number", we could say that they are all numbers without equivocation. But what I've been trying to demonstrate, is that if we allow that one is divisible, such a definition will prove to be impossible. Your example of using different bases should make this very clear to you, especially if you consider base two.
just like the base unit "one" has a different meaning in each base system
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.