sorry
.333[bar]+.333[bar]+.333[bar]=.999999[bar]
sorry 1/3 = .33333333 [R]
but what does .333333R] converge to
add three of them together and your number is bigger than 1
the proof is rubbish
as i said
I reported you for not putting any effort into that last post.
You’re wrong. If you can’t put enough thought into understanding why 1 = .999… then I’m very sorry.
colin’s just upset because if .999… converges to a number (which it does) you could ‘point to it on a number line’ and that would throw off her whole life’s philosophy.
The problem here is in the way we write these quantities out. Writing ‘1’ is a way of expressing the quantity 1 exactly and instantly. Writing ‘.999[bar]’ is a way of expressing the same quantity but by way of approaching that quantity over time - you do get there in the end though. The way we imagine this is as though it were a process - that is, we imagine 9s being constantly added to ‘.99999…’ until we get to the end. But of course, we never reach the end since that would take an eternity. But the fact of the matter is, we are always approaching 1, no matter how long it takes. The problem, though, is in that, like all limits in mathematics, it takes an eternity to actually get there. We think, therefore, that it CAN’T be reached. But this is only true for a finite amount of time (which brings us to a finite decimal expansion - which indeed is less than 1). The fact of the matter is, however, .999[bar] is infinitely long. Therefore, as it stands, it has already reached the limit of 1, and therefore already equals 1.
heres an example…
say we want to travel 4 miles east in an electric car.
the problem is that each time you can only travel half the distance that you just traveled.
the first distance you travel is 2 miles, the next is 1 then .5, .25, .125… and so on.
you will for eternity try to travel a total of 4 miles but it will never happen.
the sequence of numbers converges to 4, but still will never equal four.
similarily, if .999[bar] really exists than it is not converging to 1, it is converging to 1-(1/infinity)
i have already demonstrated why infintesimals cannot be quantified, and if .999]bar] exists (the 9’s can go on forever) than an infintesimal must exist.
once again i have shown why infintesimals are not quantified in decimal values…
don’t just say im wrong… prove me wrong…
don’t be a slave to symbols and numbers, use reason to prove me wrong, not the same old proof i have already objected to
no your denial proves nothing.
this example was made to show what actually happens when you multiply .999[bar]. i didnt use the cube example to prove anything… there was other explanations for that.
but in the same way that the cube example doesnt prove ur theory wrong ur theory dosen’t prove my cube example wrong.
if.999[bar] =1 than it wouldnt start out with a .9…
i keep concluding that you people are all slightly confused and are as a result appealing to the majority
i doubt you guys can even prove that .999[bar] exists… in the practical world it doesn’t…
the only way to represent it is like this [1-(1/infinity)]
and we don’t know if infinity really exists
I’m not sure where you’ve demonstrated that - and yes I have read through all your posts. You’ve already said the formal proof was NOT your box stacking thought experiment. What is it then? That .999[bar] = 1-(1/infinity)? Well, even if that WAS a valid mathematical formulation (which it isn’t - you can’t treat infinity as a number), 1/infinity = 0. Yes it does. You take an object and divide it into an infinit number of equal parts, each part will be 0 size. Just as .999[bar] approaches 1, 1/infinity approaches 0 - in fact, it IS 0.
just because i don’t have infinite time to write your proof, doesn’t mean that an informal one cannot suffice.
the box example is to help you understand where the infinitesimal is and how it can be quantified imaginarily…
the box example breaks the ice for someone who tries to add .999[bar] and .999[bar] together.
the latent effect is a clear view of what happens to the infinitesimal differences.
and i said… if .999[bar] exists, so must a true infinitesimal. and no number can represent it…
this can be seen in the pie example… make 3 pieces out of 1 pie and they say it cannot be a true third…
to put it bluntly, since our number system is base 10, a third of something cannot be exactly defined by a single number.
.33333333333333333[bar] would go on forever with the addition of 1/3rd of an infinitesimal at the end. that is a true third…
that is why some people seem to think that .333[bar] times 3 = .9999[bar]… they cannot have absolute precision which is why they lose infintesimals…
unlike a simple fraction… here is my mathematical proof
let .333[bar]= 1/3 <----------------- this is interesting because you cannot disagree 
(or is it you will not)
so…
1/3 + 1/3 + 1/3 = 3/3 = 1
QED
.333[bar] + .333[bar] +.333[bar] = 1
for the same loss of precision when dealing with infinites, people confuse the “9.99[bar]”-.999[bar] as equaling 9, when it in fact is clearly less than 9.
infintesimal… does it mean infinitely small or just as small as possible? this may be proof that infinitesimals are figments of imagination.
.333… suffers the same ‘problems’ as .999…
Your example of Zeno’s Paradox proves the opposite. The point of Zeno’s Paradox is not that you’re only allowed to travel half the distance (even though it’s often worded the way you described), but that you always still have half the distance to travel. We all know you can make it to that fourth mile, though.
This is part of the reason why I think space is ‘grainy’. This may affect the actuality of certain numbers, but in the mathematical sense we can still do the fun games like 1 = .999…
.99999 [R]
is not a convergent sum
if it is then tell us what .33333[R] converges to
But your box example starts off with a premise that many, including myself, don’t agree with. I think it was Anthem who pointed this out. In order to use it as proof, everyone has to agree to the premises to begin with.
If you stack those boxes higher and higher, they’re never going to fall short of the tick marks representing each inch. You can say there’s an infinitesimal difference between the tick mark and the top of the box if you want, but if you really understand what an infinitesimal is, you’d realize they can’t be added in the way your suggesting. It’s like adding geometrical points side-by-side and expecting that after enough of them, you’ll eventually see a line emerging. But this is simply not so. If you ever see a line emerging, you would have to have already added an infinit number of points, 'cause all lines - ALL lines - consist of an infinit number of points.
But .999[bar] is already a number.
I think you’re confusing certain notations for actual numbers. When we write one third out as .333[bar] or 1/3 or “one third” or whatever, these notations ALWAYS refer to the actual quantity of one third. It’s true that certain notations may be inadequate, but that says nothing about the numbers themselves (and even then, we can make them adequate by appending the “[bar]” notation to the end of “.333” - that is, “.333[bar]” means one third - exactly).
I don’t disagree with this at all.
1/3 + 1/3 + 1/3 = .333[bar] + .333[bar] + .333[bar] = 1 = .999[bar]
I say infinitely small. I don’t think there can be a small-as-possible unless we’re talking about 0. Anything that’s infinitely small is also 0.
1/3= .333333 [BAR]
so what
you say .999999[bar] convergent sums to 1
so what does .33333[bar] sum to
no we cannot… you people cannot measure the difference between .999[bar] and 1 so you assume there is none…
and is zeno’s pardox er whatever (i have never heard of it) there is no way to get to the end… thats the point of the paradox.
fun games like .999[bar] exist when people with small imaginations try to tackle big problems and lose
i know… 1 trillion infintesimals would look like 1 infintesimal… but the box example transcends numbers to show you how, where, and why infintesimal precision is lost… and i have already explained that the box example comes with other explanations… like the pie example shows that .333[bar] x 3 does not equal .999[bar]
HAH! define it…
no it says nothing about any inadequacy of numbers, merely the inadequacy of manipulationg those numbers ([bar] numbers of coarse]
way to beg the question AGAIN
[/quote]
wrong… perhaps the universe is “grainey” and there is a maximum smallest particle… or perhaps we should use practcality and just say whatever the smallest thing we can measure is an infintesimal.
once again your imagination will not let you realise the difference between an infintesimal and 0…
We’re not the ones with small imaginations.
proof
1=/ .9999999[R]
x=.33333[BAR]
3x = .99999999 [BAR]
but you say
.99999999 [BAR] = 1
then
3x = 1
now 3x-x = 1.0000000[R]- .333333[BAR]
2x = .6666666…7
“…7” means all the 6s up till the final 7 at infinity
there must be a final 7 at infinity as the final 3 from the final 0 must be a 7
)if you say there is no final 3 or 0 as the series have no end
then that must apply to .99999999[R] THUS .99999]R] =/ 1 AS THERE IS NO END TO THE 9s)
therefore
x= (.6666666…7)/2
therefore
x= .333333…35
3x=1.000000…05
therefore we have now
.999999[bar] = 3x= 1.0…5 -a contradiction thus maths ends in
meaninglessness
But you haven’t shown anything. You say that .333[bar] x 3 doesn’t = .999[bar] because .333[bar] = 1/3 and 1/3 x 3 = 3/3 = 1. But yet again, you’re forgetting that you haven’t convinced anybody that .999[bar] doesn’t = 1. So if .333[bar] x 3 = 1 it also = .999[bar]. This isn’t question begging, it’s just me not granting you one of your premises.
OK… .999[bar] = 1.
I’m afraid you’re showing a disturbing lack of imagination by not realizing the difference lies in how we conceptual infinitesimals and 0, not in the actual quantities they represent. Like I said in my first post in this thread, an infinitesimal is a way of talking about zero by imagining approaching it, but never quite reaching it 'cause the approach is always done by dividing the remaining distance into smaller and smaller parts. That’s the only difference.