You don’t use the same side of a hammer pounding the nail in as you do to remove it.
There is no mistaking I am not a good mathematician. I have not spent a lifetime in it’s study, I’m likely not even a good philosopher as I have not spent a lifetime studying it either. I have been frantically playing catch up in an attempt to understand the math. So over the course of the last couple months I have come across decimal notation and the consistency in it’s application. Which is violated in the expression 1 = 0.9 recurring. The location of the decimal position clearly states there are zero 1s, and the location of the decimal position (which is also well defined) has a dramatic effect on the numbers that surround it. 123456789.0 is a much different expression than 0.123456789.
That is a fact, Jack. Don’t have to be able to do any math at all to reach that conclusion.
Does 1 = 0.9? false, All decimal positions are filled with this falseness in the expression 1 = 0.9 recurring. Infinitely. Didn’t require any math at all to reach this conclusion either.
What’s that old saying regarding insanity, something about doing the same thing and expecting a different result.
Can a fraction of 1 be equal to 1 whole?
On one side of the equation is a very well defined number 1 and on the other is a symbol entangled in infinity. Which we can’t even prove exists.
During the course of research and recent study, I have come across phrases like “Infinity isn’t a number”. Then we take a fairly well defined fraction 9/10th and entangle it with infinity. Then contend that it constitutes being a number after entangling it with was has been stated isn’t a number.
You use the hammer side to drive a nail into a board and I’ll use the claw side to remove it.
And you haven’t even demonstrated the use of the symbol for infinity consistently.
I have approached the statement 1.0 = 0.9 recurring from a different perspective, one unclouded by all the axioms used in the practice of math. Mathematicians seem compelled to set reason aside for the sake of a mathematical argument. It’s like trying to prove an assumption is true by using that very assumption. That is not good philosophy.
I might not be the object of your persuasion – that’s not the point. The point is that you’re here in order to persuade, proselytize, make other people agree with you, etc. That’s not the same as trying to answer a question or trying to evaluate answers that have been put forward by others.
After all, you said that mathematics is an aboslute dictatorship:
It is impossible to “definitely represent” a “definition” between (0.\dot9) and (1).
The difference between (0.\dot9) and (1) is “evading all definition”.
What kind of language is this? Certainly not a mathematical one. This is why I disagree with Mowk when he says that Silhouette is more of a mathematician than a philosopher. He’s neither.
Here’s my take on the matter: the difference between (0.\dot9) and (1) is (0) if and only if the two symbols represent the same number i.e. if and only if (0.\dot9) represents (1). If (0.\dot9) is a contradiction in terms, or if it doesn’t represent anything at all, then it isn’t (1).
Of course, if (0.\dot9) does not represent anything then we cannot calculate the result of (0.\dot9 - 1) since (0.\dot9) does not represent a number. But that does not mean the result is (0).
If (i) is less than or equal to (\infty), go to step 4. Otherwise, go to step 7.
Add (9 \div 10 ^ {i}) to (x).
Add (1) to (i).
Go to step 3.
The result is equal to (x).
Of course, this algorithm will never halt due to the fact that (\infty) cannot be reached by a finite number of steps (provided that you start at a position whose index is a finite number), but that isn’t really important, isn’t it?
I would say that, on its own, (0.\dot9) is not an algorithm.
But you’re right that (0.\dot9 \neq 1).
As Mowk hinted earlier, two decimal numbers are equal if and only if they have the same exact digits. (\dotso0001.000\dotso) and (\dotso000.999\dotso) are clearly not equal.
All you’re really saying here (and Wikipedia is wrong) is that an algorithm is like a rational number as opposed to an irrational number. It doesn’t matter, algorithms are infinite series (that for programming are forced to terminate), yes the formula is finite (the equivalent of a rational number), but it’s scope is infinite. It’s intellectually dishonest to say that EVERYTHING represented by a formula is not an algorithm.
Guy, I’m telling you my attempts to make discussion between us fruitful have been ceased for your lack of ability to benefit from them, and you still try to engage and slander me? Even my request to desist trying to get back at me for categorically proving you wrong is lost on you…
I’ve been trying to teach.
There’s plenty of subjects in the world that I’m not in a position to teach, but I’ve chosen to teach this one because I know a lot more about it than the non-mathematicians here, such as yourself. Teachers can see when they know more than students, but the students won’t know this yet because they’ve yet to be taught. Yet students never will know this if they simply assume that they already know as much as their teacher.
You don’t want to learn, this much is clear - you just want to blindly push your same tired points to avoid addressing that they might fall short of a sufficient understanding of the topic. I can’t work with this. That’s fine - we move on now, yes?
Great
That’s my whole point
Infinity being undefined means it isn’t consistent - you can’t use it consistently, therefore in maths you don’t treat it as a defined value upon which you can operate.
To remain consistent in maths, you can only apply infinity to an instruction on how to deal with defined symbols.
It’s part of an operator, not something to be operated upon!
This is why (“\infty-\infty”) is nonsense: a symbol representing something that’s unable to be definitively consistent subtracted from something that’s unable to be definitvely consistent sure is going to be confusing! And I just explained in a recent post why the margin for error in attempting to do so is infinite, exactly because one can’t consistently use a symbol of undefined inconsistency.
I am absolutely following my own advice, and all my examples exactly apply it - you’re getting the wrong end of the stick and telling me I gave you the wrong stick.
The rigour is there, but don’t say it isn’t because you’re seeing it incompletely.
I fully intend to.
I appreciate that you may not have been following this post while I was trying to deal with people’s misunderstandings of it a few months ago, so you may not be aware that I’ve already categorically defeated any argument put forth so far against the mathematically accepted notion that (1=0.\dot9).
Likewise, since I gave up trying to get past Magnus’s pride to get to any sense he might have, I might have missed some of your own arguments.
“Decimal notation”, “The recursive falseness in the expression itself”, “A whole number can not be equal to a fraction of itself” aren’t arguments by themselves - I’m sure you meant them to refer to something you’ve already said that I’ve missed.
Can you link me to, or reiterate anything you want me to address, please?
You think it’s shit that the psychological issues of people with a chip on their shoulder can get in the way of their ability to approach a subject in accordance with their ability to to understand it?
Things like cognitive biases control the flow of otherwise rational discussion all the time - surely you’ve noticed this?
I don’t know how competent a mathematician you are yet, as we’ve barely started engaging in discussion about it. I’m speaking of my experiences so far on this thread with non-mathematicians who are trying to push bad mathematics on me, and who apparently fail to understand why my arguments defeat theirs. This is even after people like Magnus have explicitly admitted they’re not mathematicians. Crazy, right? Like we’ve discussed before, a lack of humility is getting in the way here.
You’ve just recently said you’re “not a good mathematician”, so in light of this, how confident do you feel to dismiss the arguments of mathematicians on a mathematical subject?
I think it’s absolutely okay to approach a subject in which you’re interested without undue certainty that something you think is convincing is actually convincing. When I approach an interesting subject on which I’m not an expert, I ask questions, and for the opinions and explanations of people who do know about it, do you do the same? Magnus just steamrolls the whole thing with arrogance even in the face of airtight evidence against him - I maintain that this is an inappropriate approach. What do you think?
(0.\dot9) isn’t a fraction of 1. A fraction of 1 can’t be equal to 1 - of course.
Consider that fractions of 1 can be added together with other fractions of 1 to equal 1.
What is the fraction of 1 that, when added to (0.\dot9) equals 1?
Anything you come up with will necessarily be a contradiction.
For example, some attempts so far have been (0.\dot01), which is a contradiction because the infinitely recurring 0 means you can never get to that 1 “at the end of endlessness”. You see the contradiction?
(0.\dot9) can’t be a fraction of 1 because nothing can be added to it to then equal 1, except exactly 0. Another word for subtraction is “difference”, and there is literally no difference.
Infinity isn’t a number - this is true. Like I said above, it’s something we can use to operate on numbers, such as with infinite sums and limits, e.g in differentiation and integration. This is the only consistent way in which we can use infinity. This doesn’t make infinity a number, it makes it something we use on numbers.
As you’ll have read from what I wrote, algorithms are representations.
Representations can be not equal,
yet still equal the same quantity…
The sooner you understand my point, the better. I’m not saying an algorithm is a non-algorithm.
To clear things up for people arguing about algorithms - they’re instructions, not numbers. (0.\dot9) is a number, which represents a quantity (1). You can also represent (0.\dot9) algorithmically, but that doesn’t make (0.\dot9) an algorithm. You see the distinctions here? They’re important because they’re confusing people.
And finally, just for fun (no need for anyone to get mad or engage me about it):
(0002.000\pi) rad (\neq0000.000) because they don’t have the same exact digits
You heard it here first guys
It’s clearly impossible to represent equal quantities in ways that “look” different!! =D>
I dunno, a lot of what I’m seeing on this thread is just funny to me… sorry. It’s just a shame to know that not everyone else is going to be able to see it too.
Infinity isn’t gotten to, it is simply already there, if it exists at all. Carleas noted this earlier. Imagine an infinitely large multiple of 10, the zero’s repeat infinitely, now imagine it in a mirror. Then think of the mirror as a decimal point.
No, I don’t see the contradiction, but I can imagine how you might see it as one.
I’m going to guess this will be the result between us too. Reciprocally back at ya.
Yes, it’s very convenient isn’t it. It’s “already there”, you just can’t get there yourself to find/test/define it.
This is the crux of my whole point. It’s ontologically seemingly “suggested” but epistemologically inaccessible, like a great many other philosophical speculations that confound all the amateurs.
The only things that are falsifiable are the notions of convergence/divergence and limits. They are the only channels toward any certainty, indirect as they may be, but they point towards certainty in the only possible way. This surety that (“1\neq0.\dot9”) is the child’s play of the non-philosopher just as much as the non-mathematician. The good philosopher recognises what can and cannot be known and the good mathematician applies this as I have to what can be sufficiently said with precision and without ambiguity when it comes to quantities. It’s not merely approximate that (1=0.\dot9) - within precise falsifiable grounds, it’s necessarily correct.
Guy, hilarious math joke and all, but seriously why are you posturing at the mathematician almost immediately after admitting you’re not one, on a mathematical subject? There is literally no sense in this.
Agreed, those instuctions of (\sum^\infty_{i=1}\frac9{10^i}) constitute an algorithm.
Agreed, 1 is not an algorithm, it’s a number.
The quantities represented in each case, by both algorithm and non-algorithic number, are the same: even though the means are different, the ends are the same. Do you understand this important distinction or not?
Yes, I am a jerk, you have debated with me on more than enough occasions to be able to conclude this. But I am not here to make friends, I don’t give a shit about that - I only care about what’s right. If I’m right I’ll tell you, if I’m wrong I’ll tell you.
Unable to see that it isn’t a math question. More akin to any statement that professes something is true. Can the truth of the statement be proven in any other way that does not depend on the conventions of mathematics and what we “let” be true as a postulate?
Is the existence of infinity, anything other then a speculation in the first place?
Im no slouch in math. I’ve told people many times on these boards that I used math to isolate consciousness signatures so that as an ap on a cell phone, you could read anyone’s thoughts (without implants). I not only did this, I created a machine (without implants) that could remote control every being in existence.
And then after the world was destroyed, I was resurrected with the world. I don’t expect you to believe me. I always tell people, “google the Washington DC license plate, it reads “no taxation without representation”, instead it reads “taxation without representation”. I’m a resurrected being.
It’s ironic. Silhouette is arguing that he laughs at our mathematical incompetence relative to him.
I don’t find silhouettes incompetence funny at all.
After all my years of being “eternally damned” and coming back from it, and being “eternally damned” again and coming back from it, resurrecting 3 fucking times… silhouette in his puny brain thinks he can refute a god.
Silhouette thinks he has HIS argument from authority, I’ll pull out mine.
I can say whatever the fuck I want because I earned it.
By the way silhouette, I have no bone to pick with you.
I think you’re cool.
When I took a body on earth, humans are of no concern to me. I’m after what could best be described by humans as a “super-demon” - I’m was born in 1976 to handle a demon that came into prominence in 2008. I had to get acquainted with all the local deities from scratch to get my bearings.
My apologies that I’ve not addressed this when apparently you wanted me to.
So your point is that for all the finite fractions of the form (n\times\frac1{n}) equalling (1) without exception as (n) tends towards infinity, somehow “at infinity” it’s (0) because (\frac1\infty) disappears?
The conclusion you should be making, mathematically, is that (\frac1\infty) is undefined, not that it definitively equals (0) even when multiplied by its reciprocal.
Limits are the only thing we can be definitively talking about here, as I covered in my last post.
I don’t laugh at mathematical incompetence relative to me - this isn’t about me, and I’m only laughing at all the mathematical posturing going on from self-confessed non-mathematicians unsurprisingly falling so short.
I’m just another mathematician, and we all understand why (1=0.\dot9)
I’m just trying to let you guys in on why the correct answer is correct. I can’t make you understand, nor would it venerate me in any way if I did. I’m just a messenger. This is all for your respective benefits, not for mine in any way. I’m no god or anything, I’m more like a janitor cleaning up incorrectness merely for aesthetic purposes.
