As you noted, we're all a little odd sometimes, just as we're all a little, actually a lot, ignorant most of the time. Ignorance yields to knowledge and information, learns in other words, else it becomes just stupidity - and some of us even arrive there from time to time. But beyond these informal divisions it gets dark quickly. Beyond the border of stupid on the other side is evil. Why? For what reason? To what end? That's often not immediately evident. And it may be the world we find ourselves in at the moment, but I am increasingly inclined to call out evil masquerading as stupidity (and masquerading as anything else), and to give that evil little or no space, or air to breathe.Meta's queer usage. — Banno
A true square does not admit to a diagonal, the two sides are incommensurable, making the square an irrational figure, just like the circle. There is no such thing as the diagonal of a square, because there is no such thing as a square, just like there's no such thing as a circle. — Metaphysician Undercover
They've proved it. — Michael
A, therefore B, where A is .999... = 1, and B is some rambling about equivalence. But here we don't merely have equivalence, we have equality. Because we have equality, they do represent the same value. I've never heard of someone so far gone as to commit an amphiboly by changing the word. But in this post, and here?: — InPitzotl
That definition was already discussed in the thread. And that definition is used in the pdf provided by the op in section 1. By that definition, .999... = 1 exactly. — InPitzotl
n other words, 65 pennies, a dime and a quarter is not worth a dollar because pennies are 1/100th of a dollar and that's not a particular quantity of money. I mean, sure, some pennies are smaller than other pennies slightly; but some dollar coins are also smaller than other dollar coins. But apparently the pennies being smaller implies that pennies aren't a particular value, whereas the dollar coins being smaller does not indicate such a thing. Such is the tomfoolery I've heard from you so far. That's a garbage argument that can be ignored just on its merits. — InPitzotl
Sure they do. 1/2 represents one half. As you said, one of anything represents a particular quantity. The quantity that half represents is very clear... that is the multiplicative inverse of two. It takes two halves to make the quantity one. — InPitzotl
The way mathematics speakers use the term "particular quantity", 1/9 is indeed one of those things. — InPitzotl
Therefore, your real burden is to show what's wrong with the language of math; you can't just say, "I don't 'believe' 1/9 is a particular quantity"... you have to say, "saying '1/9' is a particular quantity leads to the following problem" and say what that problem — InPitzotl
Well, Metaphysician Undercover hasn't addressed the two proofs from the OP. All he has done is to assert that 1/9, and other fractions, are not numbers. His argument is an appeal to the authority of the OED. — Banno
ncidentally, and to my great amusement, the OED definition of fraction is "...numerical quantity that is not a whole number...", contradicting Meta's assertion that fractions are nether numbers nor quantities. — Banno
Perhaps there is something to be gained here, not by treating Meta's posts seriously, but by looking at how he avoids confronting the truth. — Banno
For example he provides a restricted definition that suits his purposes, and when challenged he demands 'I invited anyone to provide a better definition of "number"'; a "have you stoped beating your wife" response. — Banno
Again, there is the outstanding point that he fails to directly address the two arguments presented in the OP. I think this is in order to avoid rigour. — Banno
It just shows that the definitions of mathematicians contradict themselves. — Metaphysician Undercover
He can start here: according to MU real numbers, with the exception of integers, are not numbers, and:
A true square does not admit to a diagonal, the two sides are incommensurable, making the square an irrational figure, just like the circle. There is no such thing as the diagonal of a square, because there is no such thing as a square, just like there's no such thing as a circle.
— Metaphysician Undercover
In as much as he, or anyone, can believe what they like, still, they ought not present their beliefs as categorically true. I invite him to here rigorously prove his claims, or recant and retire in silence. — tim wood
As a matter of representing numbers, wouldn't most be fine with 9/9 = 9 × (1/9) = 9 × (0.111...) ? — jorndoe
Wrong. I have. Also, Banno has:No one has demonstrated how 1/9 represents any particular quantity, — Metaphysician Undercover
...using your own dictionary. And your dictionary has, as demonstrated by Banno. Your problem is that you don't understand the language; that's confounded by the fact that you think you do.Incidentally, and to my great amusement, the OED definition of fraction is "...numerical quantity that is not a whole number...", contradicting Meta's assertion that fractions are nether numbers nor quantities. — Banno
FTFY. A ninth is the specific particular quantity corresponding to dividing one into nine equal units. That's why your same dictionary that you quoted the definition of a number in says that a fraction is a number.because as I'veexplainedasserted, it does not represent a quantity.
By proof, such as the one given in the OP.So how do you claim they are equalor equivalent? — Metaphysician Undercover
We're using your OED definition.I see no such definition. — Metaphysician Undercover
Wrong. According to that definition, they are numbers. You just don't understand that definition... see above.According to the definition of "number" which I provided they do not represent numbers. Where's your definition of "number"? — Metaphysician Undercover
That's quite interesting. What I was saying here is a direct analog of your points about fractions and pie applied to money according to my best assessment of what gibberish you're trying to push. So if you yourself don't understand this, maybe you should heed the advice you're trying to give me.Sorry, I have no idea of what you're talking about again. I wish you could make a greater effort to make clear what you want to say. — Metaphysician Undercover
It's only ridiculous to you, because you don't speak the language.Ha ha, that's ridiculous. — Metaphysician Undercover
We've already addressed this... you're saying nothing about fractions that doesn't also apply to counting numbers. To have a point you must special plead it.1/9 can be any quantity you want, depending on the size of the whole which is being divided nine ways. — Metaphysician Undercover
What are you talking about? A whole pie is one pie, not nine pies, eighteen pies, or twenty seven pies. You mean groups. Taking a particular quantity of equal sized groups is just multiplication. If I were at a farmer's market and they had a carton of a dozen eggs, I might could barter getting one half of a dozen. He'll give me six eggs. Or maybe I need more... maybe I need two dozens. He'll give me 24 eggs. Even your precious one dozen is twelve eggs. You're choking on multiplication.1/9 can be one if the whole is nine, it can be two if the whole is eighteen, it can be three if the whole is 27, it can be four if the whole is thirty six, and so on and so forth. — Metaphysician Undercover
Nope. I would say you had some severe misunderstanding of math.And if mathematics speakers really use the term in this way, then I'd have to say that they really do not know what they're talking about. Don't you agree? — Metaphysician Undercover
1/9 is only a ninth of 1. But you can take 1 of anything, including groups.How can something (1/9), which can be absolutely any quantity whatsoever, be said to be a particular quantity? — Metaphysician Undercover
Because I understand how it makes sense, because I understand it.And how can you not see the ridiculousness of the claim that it is a particular quantity? — Metaphysician Undercover
I take my definition of "number" from OED: "an arithmetical value representing a particular quantity and used in counting and making calculations". — Metaphysician Undercover
Followed byThe sum or aggregate of any collection of individual things or persons...
and then...A sum or total of abstract units...
and then on to other related uses.the particular mark or symbol, having an arithmetical value...
I found it on some random russian vocabulary site: (https://slovar-vocab.com/english/fundamental-vocab/number-6810737.html) (ETA: Unhiding this link). An expanded version can be found here.It's a slow day, so i dug out both the Concise and the Shorter OED. — Banno
I personally was granting that maybe he had one of those ancient analog thingies made of trees. — InPitzotl
I mentioned before - I don't know if you noticed it - that this thread is not about mathematics so much as about the psychology of crackpots, of which Meta is certainly one. — Banno
I suggested elsewhere that the motive might have been a search for recognition — Banno
9/9 = 9 × (1/9) = 9 × (0.111...) — jorndoe
They may have thought that they were in a discourse about mathematics, but they were in a discourse about Meta's certainty. — Banno
They think they've proved it. Staring from a false premise does not make a sound proof. But if one doesn't recognize the falsity of the premise... — Metaphysician Undercover
What I can't decide is which came first. Whether the need to respond this way promotes that kind of philosophy, or whether that kind of philosophy entices people into responding that way. If there was no form of discourse in which one could appear to argue about what a number "really is", would they invent one to meet the need, or would they be out of alternatives and have to fumble by with only half understanding like the rest of us? — Isaac
Now you've struck the heart of the problem. Some quantities cannot be divided in certain ways. It is impossible. Three cannot be divided by nine, it is impossible. Nevertheless, mathemagicians are an odd sort, very crafty, wily like the fox, devising new illusions all the time. They like to demonstrate that they can do the impossible. Some people even believe that they actually do what is impossible. That is a problem. — Metaphysician Undercover
You didn't see this? Put up or shut up! — tim wood
perhaps in answer to Tim's question you might set out where the flaw is in this calculation - regardless of wether the items involved are numbers or not, where in your view does this go wrong? — Banno
Now you've struck the heart of the problem. Some quantities cannot be divided in certain ways. It is impossible. Three cannot be divided by nine, it is impossible. Nevertheless, mathemagicians are an odd sort, very crafty, wily like the fox, devising new illusions all the time. They like to demonstrate that they can do the impossible. Some people even believe that they actually do what is impossible. That is a problem. — Metaphysician Undercover
To slice a pizza into equal slices, try a pizza cutter. Ten paragraphs of nonsense gibberish can be refuted with one kitchen appliance.In reality it is contradictory trivial to divide one into any parts, because then you are saying that it is not one, but however many parts you are dividing it into. — Metaphysician Undercover
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