.9 repeating = 1? Is our numerical system flawed?

Originally posted by Sublime620
Which is why it can't have a place on the number line - it's not a number. It's a representation of a growing/shrinking number. It's constantly getting bigger or smaller.

LOL. Why are you contradicting 00Einstein?

Originally posted by 00Einstein
Anyway, the 1 cannot exist on the end of that number. You cannot say that it started as 0.1 and you simply added zeroes in the middle infinitely, and now is infinitely growing. A NUMBER CANNOT GROW! It is static. You can discover a new number by adding to the old one, but it will NEVER be that same number changed. 4=3+1, but 4 is not a overgrown 3. It is a seperate entity.

Originally posted by Sublime620

Yes it's going somewhere. Every time another 9 is added to the end, it is getting closer to it's destiny.

Now you are claiming that the infinite number has an END?!???!?!


My have the tables turned....

Originally posted by Sublime620
reply to post by drevill

 

Universal language. You change the name we used to represent the number, but 1 will always be 1.

It represents 1, no matter what you call it.

hello

could you explain? Universal language i'm assuming is universal acceptance?? however how do you prove that the sum of One is the true representation of the figure 1?

what im trying to say is who first said this was so and how did they prove it? You cant hold up one milk bottle and say this is one as this is an explanation of the rule that has already been decided, who decided/agree the basic formulas (right word??) Also was this discovered or originally used to prove an exsisting thought or point?

many thanks

david

i don't claim to be a math genius, but i did have a few advanced math classes in high school. i don't want to pour gas on the fire, i'm honestly trying to settle this in my own mind as well.

i did some reading and i found one thing that made it sort of almost make sense to me:

You can show (using calculus or other methods) that with a large
enough number of 9s in the expansion, you can get arbitrarily close to
1, and here's the key:

THERE IS NO OTHER NUMBER THAT THE SEQUENCE GETS ARBITRARILY CLOSE TO.

Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1.

There is nothing special about .999... The idea that 1/3 = .3333...
is the same. None of .3, .33, .333333, etc. is exactly equal to 1/3,
but with each 3 added, the fraction is closer than the previous
approximation. In addition, 1/3 is the ONLY number that the series
gets arbitrarily close to.

mathforum.org...

so, according to the argument above, 1/3 is a limit that is expressed in decimal form by .3... they are not really equal technically, but they are considered equivalent since there is no other decimal that can represent 1/3. so considering .3... is an inherently "flawed" yet accepted representation of 1/3, then i suppose that we can say that multiplying by 3 gives us .9... and it's an inherently "flawed" yet acceptable representation of 3/3 and in turn 1.

it's a matter of perspective i think and i can easily relate to arguments on both sides.

this is off-topic, but i'm reminded of a neat math problem that i heard from a tour guide while visiting the Tate a few years back. it's not really related but it lets me see how things don't always work out the way we think they should:

a sultan has 3 sons to whom he has left 19 camels when he died. he decreed that the oldest would get half of them, the middle would get a quarter, and the youngest a fifth. they had no idea how to go about dividing the camels since they couldn't really split up the camels into fractions. as they were arguing a passing nomad offered a solution. he would let them borrow his camel. now they had 20. the oldest brother got 10 camels, the middle had 5, and the youngest had 4. with that the nomad rode off on his own camel.

hope that at least lightens up the conversation. =)

Originally posted by ALLis0NE
Your quote above is stated like a fact. When it is not one.

Oh but it is. How dwindling your thought to not recognize such.

Tell me of the thing that you can divide infinitely in physical reality that is not infinity itself.

----------------------------------------------------------

Remember that question? You never answered it, among a handfull of other questions that confounded your speculatory and poorly put together hypothesis. ( it in fact has no premise at all, you have flip flopped all throughout the previous 4 pages or so. )

I'm still waiting for you answer it and I will continue to repeat it until it is answered. I'd like to see some "physics specialist" skills put into action.

Well, stop dodging and let's see it.

signature
"Infinity Ends, you just will never reach it."

You're also still yet to understand the concept of infinity and the concept of finite. A few pages back I placed the definitions in a post for you. Infinity does not end. It's only limit is that it can not be limited. Finite's only limit is that it can not be unlimited.

What your signature says is cool for poetry and such, but it has no meaning to reality and physical existence. It's a straight out fallacy.

[edit on 4-4-2008 by LastOutfiniteVoiceEternal]

Originally posted by LastOutfiniteVoiceEternal

Originally posted by ALLis0NE
Your quote above is stated like a fact. When it is not one.

Oh but it is. How dwindling your thought to not recognize such.

You are lying now. It is NOT a fact like you claim.

Inside atoms are electrons and protons. Inside electrons and protons are quarks. Inside quarks are another giant mess of noise. Scientists are slowly finding out that no matter how small they try to go, there is always further. It is never ending.

Did you not know that yet?

reply to post by ALLis0NE

As the quote in your sig says, that's doesn't prove it never ends. It just proves we haven't reached the end, if it exists.

Originally posted by ALLis0NE
Did you not know that yet?

Well until you can prove yours then we're in the same boat... and ergo.. welcome to infinity and the infinite one

(although you dodged the part where I asked "tell me about the thing in physical reality that is not infinity and can be divided infinitely. It doesn't exist! Do you know what this means? That every 1 is infinity! Hooray. Will you agree now? Your "1" circle can be divided infinitely. (according to your theory/hypothesis and belief system that is purely mathematical and futuristic [there's nothing wong with that, don't take that the wrong way]).

Therefore 1 = infinity. And you see that one circle that you divide infinitely is not really "1" circle, it is only a fraction of the universe... thus an infinite fraction of the infinite universe.

And btw, infinity NEVER ends There are many things that are finite that we will never reach, that does not make it infinite. What makes the infinite infinite is not only that it can't be reached, but that it never ends or begins and that is the REASON WHY it can not be reached!

Of infinity there are finites such as Human lives that end and begin, we can also look at that methematically. Don't forget physical reality and you'll be great!

[edit on 5-4-2008 by LastOutfiniteVoiceEternal]

Hi pals,

Jus was readin the thread.. which made me chk in other websites ergarding the same ... got a few info .. chk out if it helps out ..

mathforum.org...

Ok time to end this once and for all since you all obviously missed the FACT that the decimal system is incapable of displaying 1/3 correctly.

The reason decimals get into an infinite loop, is because when you come across a number that is odd in nature, it can not split a whole number.

For example, if I want to split 5 in half.

|| | ||

There is 2 lines on one side, and 2 lines on the other, with 1 line in the dead center. With the decimal system, if you divide 5 by 2, it will take that line in the dead center and split it in half and represent it with a .5

So 5 divided by 2 equals 2.5

This was the point of decimals, to represent fractions.

When a number goes into an infinite loop, like .9... this is because the number is already on the right side of the decimal, it can not split a whole number.

The only way 0.9... would ever stop, is if there was another decimal point like this:

0.999999999999999999999.5

..but since the decimal system was not designed to fraction a fraction, it will become an infinite number. Since it can not put another .5 on the end, it will get as close as possible to doing it, without really doing it.

Does that make sense?

Let me try again:

1 divided by 3 = 0.3...
1 divided by 4 = 0.25
1 divided by 5 = 0.2


Lets say 1 = 100 smaller units.

If I divide 100 by 4 the answer would be 25 units. Because 4 x 25 = 100. Hence 1/4=.25

Now if I divide 100 by 3 the answer HAS REMAINDERS. It would equal 33 units. But since 33x3=99 you can see we have a REMAINDER of 1 that is missing to make 100. We are missing one, it is not accounted for. Where did it go? When we find it where do we put it?

Since we have a decimal system, we can take that remainder and split it in parts, and share it.

100 divided by 3 =

33
33
33
-------
99 total 1 remainder

This 1 remainder is the EXACT CAUSE of the INFINITE NUMBER.

You can take this 1 remaining unit, and "split it", and give it to each group of 33's, but even then you will STILL have a remainder of 1.

33.3
33.3
33.3
--------
99.9 total .1 remining.

So you have to split the 1 again!

33.33
33.33
33.33
----------
99.99 total and .01 remaining.

Still 1 remainder left, and to make it truly equal, we must keep splitting the 1 remainder that is left over. No matter how small the remainder gets each time we equally split it among the 33's, we have to split that remainder until nothing is left, and all 3 pieces have an equal amount.

So you see, you are dividing a remainder, over and over and over. It will never stop because you can divide things infinitely SMALL. Since there is no limit to how many times you can divide something mathmetically, it will go on forever, NEVER REACHING EQUALITY.

You asked the calculator to give you the EQUALITY when you pressed the = button. It tried to give you the equality of 1 divided by 3, but since it failed the first attempt, it will try again, and again, and again, until the remainders of the equation are EQUALY DIVIDED. This is how .3... is born.

So it is FACT that .3... is NOT a valid representation of 1/3, there is ALWAYS A REMAINDER.

When you say .9... is equal to 1. YOU ARE WRONG BECAUSE THERE IS STILL A REMAINDER OF 1 THAT HAS YET TO BE EQUALY DIVIDED.

Saying .9... is equal to 1 is like saying 99 is equal to 100. You still have the remainder of 1.

CASE CLOSED

.9... < 1
.9... != 1

reply to post by ALLis0NE


lol.

If you wanted to "fraction a fraction", say .9999...

You wouldn't need to do this: .9999.5

You just do this: .9999995

It's called a decimal system, each point has a place and is, in essense, independant from the others.

.1 is the 10s

.01 hundreds

.001 thousands

etc

I don't know what to say about a higher being that doesn't understand decimals.

If .3333333... is not an accurate enough decimal representation of 1/3, then I think AllisOne needs to explain himself, and more importantly, show a more accurate demical representation.

Thats the least you could do. If you can't do that, why are you here arguing?

reply to post by Sublime620


You got humiliated multiple times and you are still posting on here. LOL..

Ok, let me explain it for the children.

I have 100 pieces of candy. I want to give an equal amount of that candy to 3 kids. That would mean I would give each kid 33 pieces of candy, so that they don't complain about one having more than the other. Because 33x3=99 that means there is 1 piece of candy left to give to the kids.

I want to now equally divide this 1 piece of candy into 3, so that each kid can literaly have the same exact amount of candy. I put the candy on a scale, and it weighs 100 grams. That would mean I give each kid 33 grams of that last left over piece of candy. Which means there is 1 gram left over.

Now I have to get that 1 gram, and split that into 3, and share it among the children so that they have exactly the same amount of candy each. So I give each kid 333 milligrams of that candy. But still, there is 1 milligram left over to give among the children.

So, to be fair, I split that candy into 333 micrograms. But still, since 333x3=999, there is 1 micogram left over to give among the children.

So I split that 1 microgram into 3, to be fair to the children, yet there is still a remainder left to give the children. Even though it is a very very small mount of candy, I can still divide it more, and more, and more, untill there is nothing left.


But in the case of mathemtics, there is NO LIMIT. Mathematics is not limited to "physical" like grams, millograms, micrograms, and etc. It can go on forever and ever.

This is why you get the .3... when you divide 1 by 3.

This is why you get the .6... when you divide 2 by 3.

The calculator wants to keep dividing the pieces and share it among the answer. Since it is "odd" there will always be a remainder left over to divide.

.9... will ALWAYS HAVE A REMAINDER.

.9... does NOT equal 1. Sorry to burst your bubble.

Originally posted by Sublime620
I don't know what to say about a higher being that doesn't understand decimals.

I have been sitting here, correct, the entire time, and you think I don't know decimals. LOL.






[edit on 6-4-2008 by ALLis0NE]

Originally posted by ALLis0NE

.9... will ALWAYS HAVE A REMAINDER.

.9... does NOT equal 1. Sorry to burst your bubble.

Actually, 0.999... will NEVER have a remainder. There will ALWAYS be another 9 "getting put on the end" (if you tend to think of it like that, which is actually a bad example other than for such a purpose as to illustrate to someone who doesn't understand infinity) I think you need to really understand that infinity - 200 billion gajillion googolplex = infinity, and that infinity * 00000000000000000000.1 = infinity.

Simple proof that 0.999... = 1

n=0.999...
10n = 9.999...
10n - n = 9.999... - 0.999...
9n = 9
n = 1

or

1/3 + 1/3 + 1/3 = 1

0.333... + 0.333... + 0.333... = 0.999... = 1

There is NO NUMBER that you can add to 0.999... to have it equal one (except 0) because IT IS 1. If you put a limit on it and use it somewhere at 0.999...9 then it is not equal to one, and it is also not 0.999... I don't know if you know about limits or set theory, but an understanding of them will help you understand why 0.999... does in fact = 1 (if the simple algebra proofs didn't convince you)

You can enroll at your local community college for Calculus classes for about $150 bucks probably. 16 weeks is all it takes.

Try opening up microsoft calculator and typing in 1/9. You'll get 0.111... now, multiply it by 9. You'd expect to get 0.999... but you wont. You'll get 1 because 1/9 * 9/1 = 1. 9/9. We're really dealing with completely difference concepts of numbers here, so what you think is a decimal 0.999... is really not. It's a decimal with another concept appended to it.

I would explain more, but I'm pretty drunk right now. (btw, you can also get off ignoring it if you reject certain axioms of limit theory, but FYI the majority of mathematicians don't reject them out of, maybe faith. I don't know. It seems to work, but the topic is less than controversial and it is usually accepted that 0.999... = 1.)

1 - .9 = .1
1 - .99 = .01
1 - .999 = .001
1 - .9999 = .0001
1 - .99999... = ?????

I don't need a calculator to know the above answer. It just simple logic, that no matter how many 9's I add, the answer will always have a 1 at the end. Why is it only different with a never ending decimal REPRESENTATION for you people? Is it because the answer goes against your beliefs of infinity?

Originally posted by ALLis0NE Is it because the answer goes against your beliefs of infinity?

No, it's because the answer goes against the accepted, correct concept of infinity as understood my modern mathematics. It is your understanding that it flawed.

reply to post by ALLis0NE[/url]

So I split that 1 microgram into 3, to be fair to the children, yet there is still a remainder left to give the children. Even though it is a very very small mount of candy, I can still divide it more, and more, and more, untill there is nothing left.

No. According to your philosophy a thing can be divided infinitely, hence you could not ever divide it until there is nothing left. You would, by your philosophy, be infinitely dividing.

As for your "children" comment again; well we went over that already, didn't we?

And as for wanting to embarass and humiliate -people- rather than stay on the -subject matter-, well it can say a lot about a person and how much they know. There are rules here on these boards that we have to follow otherwise I'd love to be jovial and sarcastic with you and humiliate you left and right, it's what I'm best at. In fact, when I was born the PTB had to establish a jealousy committee and concentration camps for those less intellectually fortunate than I so that I wasn't killed. Then there's also the desensitizing chambers that one's are exposed to before coming into contact with me and afterwards there are debriefings. If you're ever experiencing asphyxia or hypoxia do to exposure among other cardio vascular and anatomically related horrendous reactions, just let me know. I hate watching innocents around me die in a vision resembling the fast forward of an unwatered flower as its petals begin to crumble and blacken, because they just weren't ready for the scorching sunshine.

[edit on 7-4-2008 by LastOutfiniteVoiceEternal]

reply to post by ALLis0NE


Well, just by your stupid candy analogy, you have basically admitted that .33333333... is a representation of 1/3.

Good job.

I guess we agree, and you just don't understand basic math.

(Who have you humiliated? You don't even understand fractions! )

[edit on 6-4-2008 by Sublime620]

You math guys really miss the point. The fun dosen't start until you translate the math to english statements.

What we can derive from all this is that you can accurately cut something into equal halves. Math likes that.

You can never accurately cut something into equal thirds. There will always remain a finer fraction of error than you can control.

Hmm I wonder if that's why they call those numbers odd?

Originally posted by Cyberbian
You can never accurately cut something into equal thirds. There will always remain a finer fraction of error than you can control.

Well actually you can divide accurately by any number in the real world. The difficulty is simply in representing the real analogue world in digital terms. If the approximation of a difficult fraction (repeating digits) causes a problem we resolve it by simply increasing the number of significant digits in the math processor until the error is too small to matter.

I suppose the example of thirds could be taken to the finite limit where there's just one leftover molecule but does it really matter enough to argue about it?

reply to post by Pilgrum




These people are thinking in "real world" terms. Math is theoretical for the most part.

They don't even realize that what they are arguing about is representation of the number. I've tried to explain this, but AllisOne is either too stubborn or too, do I dare say dumb, to understand.

Mod Note: Courtesy Is Mandatory.

[edit on 7-4-2008 by Dulcimer]