Alright, so you’re willing to deny even the most basic of mathematics in order to defend your asinine position, and take on an attitude as if everybody in the world is stupid except you while you do it. I don’t know why I expected more.
.1 doesn’t end in an ellipsis. That’s the point. These numbers you are pretending are so problematic can be expressed without the problematic element in any number of other ways. Fractions are one example, not-base-10 is another example. If you turn .333… into literally any of it’s other valid expression, it is exceedingly obvious why .999… is equal to 1. That’s why you resist doing it.
Respond to what I’m writing, and not what you wish I was writing. What I’m presuming is that “.333…” represents the same thing as 1/3rd, which represents the same thing as .1 in ternary, etc. I am presuming nothing about the meaning of the ellipsis on its own, I am taking “.333…” has a whole, and substituting it for some other expression that means the same thing.
There is no series. “.333…” is just a symbol consisting of seven characters which means the same thing as “1/3” or “.1” (in ternary). No infinite series of '3’s is taken to exist, or implied, or in any way relevant to the argument I am making. That the process we use to derive “.333…” (long division of 3 into 1) involves generating an infinite number of threes if we don’t stop the process at some point has fuck all to do with the value that “.333…” represents. It is, rather, a flaw in that method of deriving the value. Fortunately there are others.
“.333…” is not an infinite series. It is a seven-character symbol that references a finite value. To say that “.333…” is somehow an infinite series and thus can’t equal anything is just as stupid as saying the clause “An infinite series” is somehow an infinite series and thus can’t equal anything. “An infinite series” is a statement that has a particular limited meaning, and so is “.333…” These seven characters happen to reference the same mathematical value as “1/3rd”, and that is why “.999…”, another series of seven characters, references the same mathematical value as “one”.
Probably for the same reason that I expected you to actually read the arguments BEFORE you posted your naive first thought. Get the bur out of your ass and actually read the arguments to find precisely where a mistake in logic is being made. Trying to add your own argument wouldn’t prove anything even if you weren’t merely throwing in a naive, simple minded, already discussed argument.
Not true, because they are not numbers.
The only other “valid expression” is that of it’s infinite summation:
[list]Σ 1/(3/10^n)
or
0.3 +
0.03 +
0.003 +
0.0003 +
.
.
.[/list:u]
Note that EVERY element in that infinite list MUST end with a “3” (else it cannot be in that list). And if you multiply EVERY element of that series by 3, LOOK at what your get:
[list]Σ 3/(3/10^n)
or
0.9 +
0.09 +
0.009 +
0.0009 +
.
.
.[/list:u]
3 times your infinite list merely equals 0.999…, but 3 times 1/3 is equal to 1.000.
What that means is that you have said nothing at all. “IF, IF, IF 0.999… was really equal to 1.000, THEN we could see that obviously 0.999… is really equal to 1.000.” That is what you said.
That is called “begging the question”. It is a very well known logic fallacy. You need to come up with an actual valid argument or better, point to the actual invalid step in my logic.
I have 3 times now. How about you actually READ what is being said.
Which you were wrong about, just as I explained (and why).
No it does not. Where did you get that? The ellipsis means a particular, already clearly defined concept - “continued endlessly”. It has always been merely a convenience to accept that 0.333… comes close enough to 1/3 so as to accept it as equal. But HERE WE ARE DEBATING THE LOGIC OF THAT PRESUMPTION.
That is just wrong. I’m sure even Carleas and wtf would agree. The ellipsis in math specifically means “etcetera” or “an endless repetition of the pattern”.
Sorry, but you thinking and saying that is “just stupid”.
Get your symbols straight. Everyone ELSE seems to know what it means, just ask around, then get back us.
No, another valid expression of .333… is 1/3. Another one is .1 in ternary. If you deny that you aren’t even doing math anymore, you’re just making shit up, and I’ve got no way to respond to products of your imagination. Sure, .333… could be literally anything, or nothing, in your private universe where it’s not equal to 1/3rd.
Do you think that .5 is a valid expression of 1/2? I guess it doesn’t matter, since you’re just making shit up as you go, so maybe you don’t. But for the rest of us, for whom mathematics is a real thing that we don’t make up for the sake of convenience, .5 = 1/2. Interestingly, .5 also equals .111… in ternary. The fact that 1/2 is a repeating decimal in base 3 is no more problematic than the fact that 1/3 is a repeating decimal in base 10. Both 1/3rd and 1/2 are simple quantities that young children can understand. I imagine most any simple fraction is a repeating decimal in some base or another. 1/3rd times 3 = 1. The fact that one of the many ways to express 1/3rd is .333… doesn’t change that. The fact that you think .333… doesn’t equal one third doesn’t change anything either; you can’t prove it unless you use something other than arithmetic or logic.
We agree on the the important thing: That the only way for you to deny that .999… =1 is for you to deny that .333… = 1/3. That’s enough to prove the case to any person arguing in good faith. That you’re willing to bite the bullet and make up your own arithmetic to protect your argument is as close to victory as one gets in arguments on the internet. I’ll take it.
In a super technology of the future, where the number of decimals matters to accord the degree of accuracy, say one thousand decimals right of the decimal points, the fact that a guy in Japan tried to resolve pi as bound, using an advanced supercomputer, and failed, says volumes of the need to find such.
Merely closing the argument, does nothing to find a boundary, by declaring the value of pi. Do you see where this is going? .999999999 is open until closed. If there is only 9’s ad perpetuam, it never can really be said to be closed , regardless of how many decimals the sequence is carried foreward. If the technical requirement demands a certain degree of accuracy, a mathematical equivalency can not be assumed.
That is your premise. And that is unacceptable as a premise for the reasons that I have given. So if you want to do anything other than be rejected, you need to drop that premise and come up with one to which we can both agree.
And also, as also stated repeatedly, as long as you merely attempt to provide a proof in your preferred direction without finding the flaw in my proofs, you aren’t actually making progress.
I will agree to that as a premise if you wish. As I stated (repeatedly), if the expression ends with an “…” ellipsis, then it isn’t actually a number, otherwise we can talk.
How would you know? You haven’t read my 4 proofs:
Plus the Fifth Proof that phyllo cannot find anything wrong with them, QED.
There shouldn’t be any question that Zeno, Archimedes, Aristotle, and the like were brilliant men. And very often brilliant men are misrepresented and misunderstood. Zeno brought out an interesting issue that obviously fools a great many. But reality has no actual paradoxes, which means that he made an error (and it turns out to be a simple minded one once you know what it was). Perhaps it was intentional so as to get people to think … or to distinguish those who do.
Precisely.
But what is sad/bad is that actual logic debate is being completely forsaken so as to support contemporary superstitions. And this issue of declaring that 1.0 = 0.999… is exactly what a “superstition” really is. It is a superimposed “stitching” of concepts so as to bridge a gap in understanding and conclude a quandary. It is related to the expression:
[list]“You don’t know your ass from a hole in the ground.”[/list:u]
…meaning that the person doesn’t realize the difference between their stubbornness (ass) and the gap in their under-standing (“hole in their ground work/Logic”).
Logic debating can resolve that issue. But then there are SO very many people who fear resolution and reality.
What are you, Ecmandu now? A universally accepted conclusion of middle-school level arithmetic is ‘my premise’ to be compared on equal ground to whatever the fuck is bouncing around in your head?
No, One divided by three = .333… is not ‘my premise’. If you don’t accept basic math, I can certainly understand why you wouldn’t think .999… = 1. There’s probably all sorts of basic shit you get wrong if you don’t know how fractions work. But how does that affect me? My argument is based on universally accepted arithemetic, your argument is based on some shit you made up- I feel zero burden of proof. In the absense of any argument from you.
One divided by three = .333… is an unacceptable premise? You think you have reasons why simple division is inadmissable in a conversation about math?
That’s an impossible scenario. If you’re willing to casually dismiss 6th-grade level short division to defend your premise, you will dismiss literally anything and everything that doesn’t fit your conclusion. It’s obvious that the only way I could not be rejected by you is to agree with you.
See above. If “What’s one divided by three?” is controversial to you, you don’t belong in a conversation about math. I have no interest in trying to find ‘a premise we can both agree on’ with somebody who is already rejecting arithmetic. How could I possibly do that anyway? If you don’t know what one divided by three is, do you know that ice is frozen water? Do you know that A +B = B + A? How can anybody possibly be expected to meet the standard of ‘providing premises James can agree on’ when james can’t agree on the conclusion of dividing one digit numbers?
Of course I’ve made progress. I’ve given the reasonable people in the thread additional reasons to accept .999… = 1. I’ve been here too long to have set ‘make James change his mind about something’ as a goal.
The same procedure that shows 1/2 =.5 shows that 1/3rd equals .333…
If not, what does it equal? 1/3rd is just a magical fraction that can’t be converted to a decimal? 1/3rd doesn’t have a value? People can’t divide things into threes?
It’s also the result of an operation 3(1/3). That’s the thing about numbers; there’s an infinite number of operations that can have them as a conclusion. What’s the significance in focusing on one when there are others?
Wait, is it an operation, or a series of operations? If it’s a series of operations that can never be completed, then nothing is the conclusion of it. It makes no sense to talk about the ‘result’ of an infinite series of operations, that’s incoherent. 3(1/3) isn’t an infinite series of operations, though. And it results in .999… as well. Or 1, if you prefer.
.999… is not an operation, it is a number. At some point in your proof you confused one for the other. You’re talking about the operation never reaching the sum of one, but we’re not talking about some operation (or infinite series of operations) you chose, we’re talking about a number. And that number can be achieved with operations other than yours.
If I wanted to, I could say that 2 is the result of the operation
1+
.5
+.25
+.125
and so on, adding half of the previous amount, drawing infinitely closer to 2 but never reaching it, and then try to preposterously argue that 2 isn’t a real value. That’s all you’re doing here- picking a preposterous method of allegedly reaching .999… that doesn’t actually reach it, when their are other ways of reaching it, and then trying to conclude something about the nature of .999… on the basis of it.
First of all, according to your past arguments, “0.000…1” isn’t a number, so the difference between 1 and .999… doesn’t have a value, which means they are equal. Second, since numbers can be derived with multiple operations, the fact that one particular one leads to an odd result doesn’t mean much.
3)
0.999 = real number
“…” = infinite, non-real number
[/quote]
.999… isn’t an infinite non-real number, it’s a value equal to one. For the same reason that .222… in ternary is equal to one-half.
4)
1.0 is a “bounded decimal”
0.999… is an “unbounded decimal”.
The same number cannot be both bounded and also unbounded. QED
[/quote]
Of course they can.
You seem unaware that this very subject is debated on PhD level mathematics. And you seem unaware that when you go to the university level majoring in mathematics, you get to relearn what you thought that you learned in elementary school, such as how to count (Theory of Numbers) and basic arithmetic and equations (Algebra). In post-grad, you get to learn it all again. In those courses, you discover not only that everything you had learned wasn’t necessarily perfectly right, but also why those things are believed and taught. You learn of the fundamental theories behind the elementary school lessons. And as with all theorizing, Man makes mistakes. So some extremely simple minded issues get debated, such as whether 2+2 really equals 4, or whether the Earth really is flat (which you seem to favor).
It’s hard for me to believe that your comprehension of logic is so minimal. You don’t even know what a premise is??
No, it’s based on elementary school arithmetic, as you stated earlier.
You are suffering from a common problem in thinking that everyone around you is the same as you or very certainly much smarter or if it isn’t very clearly certain and they disagree, they are much dumber than you (rather than examining the details of what is being said with the thought that perhaps there is something you have always missed). You appear to be just barely qualified to discuss this subject, much less debate me concerning it.
Yes, I gave you reasons. I gave the reasons before you entered this … echmm… “debate” (which you failed to read). And as you stated, “I am not going to give them again”.
The issue is that you are not looking at the precise details, but presumptuously regurgitating whatever you learned in elementary school as absolute holy doctrine.
If you cannot defend it, you don’t belong in a discussion about proofs. No one cares what everyone was taught in elementary school (Hell they have been wrong for 10,000 years yet always thinking they were right).
That does seem to be the issue.
No, it does not.
!/2 is a ratio that can be represented in decimal form (noted by the termination of the long division).
1/3 is a ratio, much like Pi, that can never be represented in decimal form (noted by the inability for the long division to come to a conclusion).
One of a great many (most mathematicians could tell you that).
1/3 has a value.
0.333…" is NOT a value, but an explanation as to why 1/3 isn’t being properly represented.
That is why they are not equal; “0.333…” is not a number.
Quite the opposite.
Non-sequitur (even if you weren’t wrong).
When you add a non-number to another non-number, you grant the opportunity to form a number, much like adding wheels and an engine to the frame and cab of a car to form an actual car from what wasn’t a car.
It doesn’t matter how many invalid arguments you make. Try coming up with a single valid argument.
Your [erroneous] presumption.
Logical contradictions are not allowed in this debate.
It is now evenly balanced with seven voting for and seven voting against. Though that is actually irrelevant because the truth value of a proposition is
determined by how valid it is rather than how popular it is. For one does not demonstrate a mathematical proof by invoking argumentum ad populum
True. However, the proof is in the pudding here, since the Kantian syllogism, as is in the case of most philosophy consists of is, how it ought to be, and not how it really is.
The thing is, the importance is vested in not only interpretating , but in changing the course. The reasoning for that line of argument here, has been founded on a principle unique to Nietzche, ( and Marx), that evaluating it is beyond the principle of evaluation, as to which is right or wrong; or good or evil. There is no way, to reverse the course of that way of thinking, in a sense it is irreversible . Therefore all philosophical/logical/mathematical investigations are based on determinations which hinge on belief.
Given, that the audience here is not representative of the mass population, the argument can be made, that at least for now, the only conclusion which can be made, is that what is factual: that 1=.9999999
and it’s negation , share congruence with Kant’s categorical imperative. Where there is an even split,
between what is, and what ought, a synthesis is required, so as not to cause a total nihilization of any corresponding argument.
Total nihilization of the argument will cause a breakdown , of all abstract reasoning in terms of all kinds of languages.
A total nihilism resulting, will be deemed as unsatisfactory, in the least, and catastrophic at the most.
Therefore, what ought to be, needs to be restructured from a virtual understanding to a real understanding.
A pure understanding is what it’s all about, categorically, and absolutely, but only through the apprehension of the absolute bases of logical, semantical, and mathematical argument.
