Is 1 = 0.9999......

[MadRat]

People built bridges before the idea infinity. What's your point?

 

[spidey07]

My point is you are trying to use concepts that do not exist in the natural world.

What is math really? Just a set of rules and concepts that apply to the world around us. Philosophy is all fine and dandy but has little to do with the point at hand.

 

[MadRat]

But philosophy does prove that .999... either does not exist or if it does then it is not equal to 1.

 

[RossGr]

But .999... doesn't exist in the same respect as 1

I am sorry but I totally disagree with this statment. I can concieve of it, therefore it exists. I can represent it, therefore it exists. I can show that it occupies the same point on the number line as 1 therefore, not only does it exist it equals 1.


When I say that I can concieve of it therefore it exists, I am totally serious, I can imagine a never ending string of 9s. When dealing with the real number line the natural question is, where does it fit. I can use sound and carefull logic (inspite of Silentrunning disagreement) to show where it is located.

Silentrunning needs to address my proof directly and demonstrate the error, or he needs to read it and attempt to understand the methods and the meaning. This is the type of proof done in Upper Divison Math Analysis courses with reguarity. (I am sure Dr. Parks would be proud of me!)

 

[RossGr]

Originally posted by: MadRat

[ I]Originally posted by: RossGr[/i]
Matrat are you tottal blind? Or can you simply not read?
My final result DOES NOT RELY ON .99... + or - any thing! It shows that .999.... is standwitched between 1 and ANY NUMBER added to or subtracted from 1. There is ONLY 1 number for which this can be possibly true, 1. I have shown that .999..... satisfies this conditon.

I have shown that ANY number added to .999.... results in a number bigger then 1. I did not specify anything other then the fact that it is greater, are you arguing with that?

But .999... doesn't exist in the same respect as 1 so its impossible to find the difference. If they were comparable then you could add the difference of 1 and .999... back to .999... to make 1 again. However, since you cannot even agree that ".999..." does end in a 9 at the infinite spot then how can you even begin to understand your fallacy?

When you subtract 99 from 100 there is a remainder of 1. We subtract from the righthand column first, taking a 9 from a 0. This isn't possible so we steal something from the 10^1 digit to the left of the rightermost "0". In this case its another 0! So we take the "1" from the 10^2 column and turn it into a zero, the 10^1 value now becomes a "9" and the 10^0 value becomes a "10". Nine from 10 results in a remainder of 1! So 100-99=1.

We can also do this with 1-.999... to deduce that the answer is a remainder of 1 at the point of the infinite (10^-n, n=infinity) decimal place. There is no universally recognized symbol for this value, nor can mathematically trained individuals like yourself even relate to the simplicity of its definition. Just as .999... would be the point theoretically closest to 1 without reaching it, .000...r1 would be the point closest to null without reaching zero. Somewhere in the last two decades the translation of infinity turned into a meaning ripe of counter-intuition. Just because it sounds good to say ".999... should be 1" doesn't mean it is remotely true.

Matrat, why are you so locked on to this 1-.99... computation, I agree that is a dicy operation, which is why I avoided doing it. If you study my proof you will see that I only add and subtract numbers of finite length. I seperate the sum to infinity with aknowledgement that is is simply non zero. Can you really argue with this?

I have shown the .99.... exists inside of a box, but the only number which can exist inside of that box is is 1.

There is a link upstream which details the meaning of this process, I have simply constructed the box.

 

[josphII]

Originally posted by: MadRat
But philosophy does prove that .999... either does not exist or if it does then it is not equal to 1.

this might be the stupidest post in this whole thread. actually i take it back but its up there.

if it does then it is not equal to 1??? what horsecrap! and fyi philosophy never proves anything

 

[MadRat]

And I've already demonstrated that if that point exists in your opinion why it cannot be an equal of 1.

If .999... exists then .000...r1 also exists.

You ignore the reality of basic mathematics to deduce something that did not actually exist. Even at the most complex level your proof does try to show that the difference from .999... and 1 cannot add up to anything but zero when it can actually equal the .000....r1 value. You resort to questioning the education of the opposition which is a clear signal you've reach your own personal limit for argument's sake. Game, set, match.

 

In my opinion, this is really a matter of definition. Infinity itself is not some concrete object. It's an abstract object and an invention in some people's opinion. The problem is people seeming to have different perceptions or definitions of infinity.

And it would seem to me that 1 = 0.99.... is a matter of definition once again. Even in undisputed mathematics, "equal" is defined differently in some mathematical discipline. For instance, equal in abstract algebra wouldn't necessarily be the same as equal in all of linear algebra. It is definition we are limited to. And when someone defines something, we cannot argue about the theorem and corollary stemming from it, as there would be only one truth if it is well-defined. We can only refuse to stipulate to the definition.

Again, this discussion has gone beyond technicality and gotten philosophical. One side is siding with the idealist who think anything can be made up--so long as there's consistency and it helps solve our real world problems--since mathematics is a fictional story line. The other side is arguing that there's only one truth to mathematics. In spite of definitions given which suggest that it's an invention instead of a discovery, people are still arguing as though it is an abstract truth that 1 = 0.999. . . . This is a philosophical question. And until you accept that fact, this discussion will never move a step ahead in progress. Well, I must admit that philosophical questions always seem infinite. LOL!

Here's a link for you guys still arguing: Is 0.999... = 1?.

 

[RossGr]

Originally posted by: josphII

Originally posted by: MadRat
But philosophy does prove that .999... either does not exist or if it does then it is not equal to 1.

this might be the stupidest post in this whole thread. actually i take it back but its up there.

if it does then it is not equal to 1??? what horsecrap! and fyi philosophy never proves anything

Good point JosphII, in the first part of the statement he claims proof that it does not exist, in the second, he admits that it might exist... I thought he had proved that it does not exits! Talk about wanting it both way.


Madrat,
For the umpteenth time, an elpsis in the middle of the number, as you have written it indicates the omission of a finite number of digits, only when it appears at the end of the number does an elipsis indicate continuation to infinity. I must insist that the notation be used correctly and consistently. If a number terminates it is does not have an infinite number of digits, again we must be consistent to have any meaning at all.

 

[RossGr]

luvly,
Guess you missed the part of your Real Analysis course where infinity was defined as an extension to the real number system.

Not only is the meaning of the term well defined the result of the basic operations are also spelled out.

I sure wish nonmathematician would admit that they do not have a clue about the finer points of Mathematics and stick to arguing stuff they understand, whatever that may.

I have never seen Emanual Kant, therefore you cannot use his thoughts in an disscussion, he does not exist, his words mean nothing.

Edit:
Have reread Luvly post, have to add,
Seems you have the two groups a bit confused, I insist that .99.... can be concieved of, exists and can be dealt with consistently and correctly. Madrat seems to be claiming that it simply does not exist.... but it might.. Go figure.

Since we are dealing with matters of Real Analysis, should we not use the definition of equality defined in Real Analysis? Why confuse the matter? We need to be consistent.

 

[MadRat]

Originally posted by: RossGr
I have never seen Emanual Kant, therefore you cannot use his thoughts in an disscussion, he does not exist, his words mean nothing.

Which seems to sum up pretty much the way you see the rest of the world when you try to exclude people by using your credentials.

You might find your credentials are but petty to your peers if you put them out there for the rest of the world to jeer at.

 

[Zebo]

Emmanual kant belongs in an Iraq thread. Not here.

Good work RossGr, Do you know the page where you showed the proof?

 

[RossGr]

Carbonyl,
Thanks, I have been through this argument so many times now it is nearly automatic.

Fresh link to the proof

 

[RossGr]

Originally posted by: MadRat

Originally posted by: RossGr
I have never seen Emanual Kant, therefore you cannot use his thoughts in an disscussion, he does not exist, his words mean nothing.

Which seems to sum up pretty much the way you see the rest of the world when you try to exclude people by using your credentials.

You might find your credentials are but petty to your peers if you put them out there for the rest of the world to jeer at.

Where have I posted my credentials?

Are you referring to the fact that I keep refering to Real Analysis courses or that I mentioned a Prof? I will not deny having had University level math courses, how else did I aquire the understanding necessary to correctly deal with this matter. As for the reference to Kant, I was attempting to present YOUR view.

 

[MadRat]

Try not to tell me to show where you said something after you've edited the post.

You've done your share of claims that other people don't make sense because they don't have your credentials.

Here is an example:

Originally posted by: RossGr
I say you have only had a basic course in calculus because that is the level of misunderstanding that you are displaying.

 

[RossGr]

Because I give the credit for perhaps having had a math course, I am making a statement on my credentials? Strang way of thinking about it. The fact of the matter is this entire topic is one that cannot be properly discussed unless you have had math beyond Calculus. Simple fact.

I would assume since you have moved from disscussing the topic to ad homine (however you spell it! I am a mathemtician, not a English major attacks that you have conceded the argument.

 

[RossGr]

BTW:
I have not changed any post via edit. any editing I have done as been appended following the word edit.


Also, upon reading my proof (I wrote that up some weeks ago) I have found some typos. All of the sigmas in the last equation on the first page and the first equation on the second page should be multiplied by 9. my apologies for any confusion this may have caused.

 

[MadRat]

Actually I only pointed out your argumentum ad hominem. Was I to mistake your poisoning of the well (by your requirements for an opponent to have had higher math) as anything but penis flapping? Excuse me while I look over my shoulder at the wall of books on the shelf. Yep, yep, all these books collected over the years of school must be my imagination. Yep, yep, none of them there college courses must have really happened...

 

[SilentRunning]

What have I learned.


1. I have learned that in the approximately twenty years since I graduated from college that RossGr has found the finite value that infinity represents.

2. I have learned that calculus is no longer based on approximations it is now able to find exact "limits" (note limits are no longer approximations see number 1.)



I guess you learn something new each day. I think I will file this away with the information a college student recently told me:

That our astronauts now train in an anti-gravity chamber. He saw it on television. (my guess is this has something to do with RossGr finding the finite value of infinity.) I tried to convince him that what he saw on television was footage from inside the "Vomit Comet" but he insisted is was an anti-gravity chamber.

Time to take Bleebs advice.

Originally posted by: bleeb
forget all this math crap and become a retarded porn star

Does anyone here know where a 40 ish male can find an open slot. (bad pun intended)

 

[RossGr]

What the heck,
you want my credentials? Why not

BS Physics OSU 1977
BS Math (With Highest Scholarship) OSU 1984
In addition I have completed 2yrs of Graduate level course work in Mathematics, at Lehigh U in Pa and at OSU.

I failed to complete my Masters Degree.

Laugh away.

 

[MadRat]

I never laugh at penis flapping.

 

[RossGr]

1. I have learned that in the approximately twenty years since I graduated from college that RossGr has found the finite value that infinity represents.

And just where have I done this?

This is really begining to sound like an engineer.

Text2. I have learned that calculus is no longer based on approximations it is now able to find exact "limits" (note limits are no longer approximations see number 1.)

so you cannot comphrend that the symbol .99.... does not represent a limit? This is something you need to deal with, the error is yours not mine.

 

[mithrandir2001]

Is 1 = 0.9999...?

It most definitely is not. Zero point something is not integer one.

 

[SilentRunning]

Originally posted by: RossGr

1. I have learned that in the approximately twenty years since I graduated from college that RossGr has found the finite value that infinity represents.

And just where have I done this?

This is really begining to sound like an engineer.

Text2. I have learned that calculus is no longer based on approximations it is now able to find exact "limits" (note limits are no longer approximations see number 1.)

so you cannot comphrend that the symbol .99.... does not represent a limit? This is something you need to deal with, the error is yours not mine.

I have tried to be careful when discussing infinity to state that you approach it not that you equal. You, however, like to say that a number equals infinity.

And you don't comprehend that it 0.9999... has no meaning. We can give it a meaning by finding its limit.

And for the record does that anti-gravity thingie really exist like infinity.

 

[RossGr]

And you don't comprehend that it 0.9999... has no meaning. We can give it a meaning by finding its limit.

Sorry but I have to disagree, look at my proof, I gave it meaning and position without taking limits. Perhaps you need to read the proof and thing about it for a while.