It’s not cherry-picking.
By the way, your posts would have more value if you tried to counter existing arguments or provide your own instead of constantly complaining about non-mathematicians.
Here’s another way to put it:
The long division ends when we reach the point at which every subsequent digit is equal to (0). That is when we can discard the remaining value, since that’s the point at which it attains (0). But with the long division of (1 \div 3) this never happens. There is no point at which every subsequent digit is equal to (0). Hence, there is no point at which we can discard the remaining value. We can’t even do it at the point of infinity – the digits that follow the infinity-th digit are not (0)s, they are (3)s.
And yet the arguments have remained unaddressed. Go figure.
What fraction of decimal notation is being ignored?
Where do you find a statement of truth within a infinite string of false results.
When has 1/3 been resolved to a definitive result?
Okay, long division of 1/3.
The pattern can easily be seen to repeat : [attachment=0]Division1over3.JPG[/attachment]
What’s been unaddressed?
No fraction of decimal notation is being ignored.
In every discipline, if you can’t “get there to see it with your own eyes”, logical extrapolation with zero margin for error is the best you can do and in many ways better than seeing it with your own eyes because it shows any other answer to be necessarily impossible no matter how far you looked with your own eyes. How things seem to look at first with your own eyes is the whole problem here, and that’s what maths is for - a surgical tool to unequivocally surmise beyond the superficial. This is exactly what philosophical argument does too - it’s basic Epistemology.
Nothing is considered to be mathematically proven until the logic is laid out exhaustively and completely to cover every possible permutation that could ever exist. Just as calculus proves gradients and areas in this way, its use of limits extrapolate to conclusions with zero margin for error. It’s no coincidence that all attempts here to show that some remainder “looks like it ought to be there” are falling foul to simple logical mistakes/contradictions.
Calculus isn’t “merely an approximation” that “might be a little bit bigger or smaller we dunno”. It’s as precise as anything can get and certainly more precise than how things might appear to a non-mathematician.
Just like with this topic it uses infinity as an operator to arrive at precise results. As I covered a seemingly infinite amount of times already, the undefined is being used exactly for its property of not being defined, without defining it, and never as a value except to communicate that any resulting value would be undefined. For infinity, the best you can do is define the way it is constructed without actually completing the construction - as in the ZFC axiom of infinity at the foundation of mathematics. Pointing out the precise beginning of a definite path isn’t the same as completely defining all of the path.
And yes it is cherry-picking to try to use and talk about math to prove non-mathematician intuitions about how things seem to appear, only to conclude that math must be wrong in some other way than how you’re trying to use it - just to fit your suspicions - when all math is inextricable interlinked. Criticising the parts you don’t like while using the parts you do is practically the definition of cherry-picking (:
And now I will cut to the chase:
1 = 0.9 + .01 = 0.3 - .01 This looks true.
1 = 0.99 + .001 = 0.33 - .001 This too
1 = 0.999 + .0001 = 0.333 - .0001 and this too.
You can get “here from there” by being a very meticulous accountant.
This >1 = (0.\dot9)< is false.
and this > (.\dot0)1 = 0< is also false.
And that is how math is performed with recurring digits.
ILP’s very own mathematical proof that 1 is not equal (0.\dot9)
At any point in the decimal notation you realize that 1/3 will always leave a remainder that is part of “1 whole” too much which is exactly the same part of the “1 whole” the fraction (0.\dot9) is missing which is accounting for all the infinite parts of 1 whole, such that the sum of all “of the parts” is always equal to the whole.
OK Phyllo, I’m done editing (I think) at least for now.
Who the heck knows what you’re trying to say?
Each section evaluates to a different value : 1, 0.91, 0.29
Phyllo, give me a moment to account for what has/is taken/taking place.
I’m “checking” the math …
Check back to that post in a few minutes, I paused before I was finished to make some breakfast. I can’t do it all at once. Well the math takes place all at once, but the checking in combination with preparing some breakfast takes some time.
As an editor, I’m also checking how well the words chosen match up with the idea I’m trying to convey, and attempting to insure I haven’t included any typos.
As an additional thought that took place somewhere between a bite of toast, a bite of egg and a sip of coffee; I got someone else to do the math and added the logic that was missing.
Thanks for all your help.
All three lines are obviously false and for the same reason. Each section, left, center, right, evaluates to a different number. They are not equal.
Thinking…
Yeah, yeah. I’m onto something… I just haven’t expressed it clearly.
[attachment=0]Phyllo+Mowk.jpg[/attachment]
I’ve expressed some ideas within that I lack the math language fluency to convey.
This is a 4 years old thread and arguments put forward by the original poster, James S. Saint, have yet to be addressed.
Most people won’t change their minds UNLESS consensus changes as well.
It’s OK Magnus I rarely make any sense anyway.
Consensus according to current poll being… ur view? (Albeit slowly changing as mathematicians get involved to provide logic…)
Shoot yourself in the foot more. It helps the consensus change towards sense!
Name one JSS argument that hasn’t already been proven wrong.
Pick any. Not a single one has been proven wrong.
When does long division end?
Hopefully, people will agree that:
- long division does not end at an arbitrary point (“whenever you want”)
- long division does not end after a fixed number of steps (e.g. after 10 steps or after an infinite number of steps)
Long division ends when we reach the point at which every subsequent digit is equal to (0).
By using long division to calculate the result of (1 \div 3), we can never reach such a point quite simply because there is NO such point.
And when I say we will NEVER reach it, I literally mean never, as in, not even after an infinite number of steps. (Of course, in order to accept this, one would have to accept that infinities come in different sizes. Otherwise, they are not qualified to discuss this subject.)
This does not mean that long division works. It does not even mean that long division has limits. Rather, it simply means that the base-10 number system cannot represent (\frac{1}{3}).
Phyllo and others who use long division to support the claim that (1 = 0.\dot9) are doing the long division improperly by ARBITRARILY stopping it at the point of infinity. You can’t stop it at the point of infinity because the point of infinity is not followed by an endless string of zeroes.
The long division argument is sophistic. It looks like it’s a good argument but it isn’t really. It’s what ooccurs when you don’t think through things. (It’s what Silhouette and Gib mean when they speak of people being deceived by the superficial.)
And that’s how you demolish the long division argument.
What’s left of it?
And of course, to say that refusing to accept that (\frac{1}{3} = 0.333\dotso) renders the entirety of mathematics broken and useless is to catastrophize.
So you mean there isn’t an end to endlessness? 
Teach us more about infinity, Magnus!