Is 1 = 0.9999......

[Haircut]

And I've already pointed out that you cannot add to a sum that equals infinite, regardless if you use it to represent an infinitely small (10^-infinity) or large (10^infinity) decimal. You want to use a rule of thumb to reason out infinitely small numbers when infinite doesn't follow the same rules as other numbers. Your argument is akin to someone insisting that division by zero is possible. Hence the conclusion of your proof has a gaping wound:

WTH are you talking about here? No one is trying to add to a sum "that equals infinite" as you put it.
RossGR's proof is completely valid. I also posted a version of this proof way back in the thread.
Please show which step of this proof is not valid with a clear and mathematically sound reasoning.

 

[yoda291]

Originally posted by: silverpig
infinity + infinity = infinity

Oh, and as to your physics problem: You can't define a position infinitely far away from another. Even if you could, the object would never hit the earth as it started out infinitely far away.

Why don't we all work on finding the non-500 page solution to Fermat's last theorem? I'll even go so far as to do the first step: Writing out the problem.

For any (n, x, y, z ) | n, x, y, z E I, n > 2, solve:

x^n + y^n = z^n

Bah, That's easy. x=1, y=0, z=1 for all n>2

BTW, I know identity equation doesn't count so don't flame me for not understanding the problem. Is joke.

I wonder how long this thread is going to be.

 

[RossGr]

Errr, nobody denied the existence of any place on the number line other than you specifically saying .000...1 cannot exist. I just said you have the problem that it either exists to disprove your point or it does not exist, but I never made the call. The problem is comparing apples to orangles, subjective values <> objective values.

Goes to show that you can prove anything when claims are taken out of context. It has been said by myself and others that the symbol .00...0001 where the ellipses represents an "infinite" number of zeros is not a Real number. I have no clue what it is, but it is NOT a real number. Correct use of the ellipsis in that context implies the existance of an unspecified but FINITE number of zeros. Using improper notation does not make a proof.

And I've already pointed out that you cannot add to a sum that equals infinite, regardless if you use it to represent an infinitely small (10^-infinity) or large (10^infinity) decimal. You want to use a rule of thumb to reason out infinitely small numbers when infinite doesn't follow the same rules as other numbers. Your argument is akin to someone insisting that division by zero is possible. Hence the conclusion of your proof has a gaping wound:

This just goes to show that you either are not reading the proof or are simply incabable of understanding basic mathematical operations. I NEVER add ANYTING to infinity or to digits AT "infinity". All of my operations are done on finite number of FINITE length. My use of the infinite tail of nines is the fact that it sums to a value greater then zero. Do you disagree with that?

If you would simply drop your preconcieved notions and make an honest effort to understand what is presented, you may enjoy an moment of epiphany.

 

[spidey07]

The universe revolves around the earth and .999... != 1

 

[silverpig]

Okay, how about instead of another proof, I just try to explain it a different way?

Let's look at this sequence:

n1 = 0.9
n2 = 0.99
n3 = 0.999
etc

For any finite number n, this sequence will always be less than 1. You can also easily see (and I don't think this is being debated), that the LIMIT of this sequence is 1. This sequence approaches 1, but is always short of this limit. I'm sure we can get everyone to agree here.

Now, 0.999... is the representation of n = infinity. Of course, if you have any finite n, you will never reach infinity, so you can say that 0.999... is the limit of the sequence. You never actually ever have an infinite number of nines if you try to follow the sequence.

Now that we have defined 0.999... to be the limit of the sequence, we can look back to our first statment, that the limit is 1.

 

[MadRat]

But being the limit doesn't mean it is equal to it.

 

[MadRat]

*rereads RossGr's proof*

Originally posted by: RossGr
If you would simply drop your preconcieved notions and make an honest effort to understand what is presented, you may enjoy an moment of epiphany.

Wow, that was convincing! You've done it!!! Err, not. The same nastly little error sticks out.

Epiphany may be the word you mean, but "indoctrinated" would be more like it.

 

[silverpig]

Originally posted by: MadRat
But being the limit doesn't mean it is equal to it.

Huh?

If I AM 6 feet tall, does that not make me EQUAL in height to a stick 6 feet in length?

 

[silverpig]

Let me re-phrase:

If 0.999... is the limit of the sequence, and the limit of the sequence is 1, then the obvious conclusion is....


If a = b, and b = c, then a = c.

 

[chrisjor]

If this were Fatwalllet..... .99 = you are getting screwed if the deal was 1.00!!!!

 

[HomeBrewerDude]

what is the limit of this thread?

 

[RossGr]

Matrat,
It is indeed a matter of definitons and the structure of the real line. Sorry if you do not agree with the treatment given this problem by mathematicians. The fact that it yields consistent results and provides a useful and meaningful tool to scienticts of all fields evidently means nothing to you. But then you have no need of this structure so it has no meaning to you. Of course you cannot realize the beauty of what you see, you simply do not understand it. Your view, from a easy chair with no need of higer math does not require an understanding of the number line. Like a blind man in an art gallery you have no concept of the beauty surrounding you.

 

[MadRat]

RossGr, you don't even begin to understand. You never did stick to the argument. Instead you want to make it personal. I do pity you.

 

[RossGr]

Save your pity.

I am waiting for an explaintion of the errors you claim are so obvious.

So now my acknolwedging that you have no need of the level of mathematical knowledge required to understand and appriecate the methods used by mathematicians to handle these issues is an insult. ...You certianlly are easily insulted. I was attempting to recognize some diversity in this world.

This is all your loss, not mine.

Pearls before the swine.

 

[MadRat]

Funny how you say I have no need for mathematics. Quite the contrary. Math is important to my work, thank you very much.

I don't pity you because you believe .999...=1. Actually I pity you because you do not keep to the syntax of what you studied.

 

[Haircut]

Originally posted by: MadRat
But being the limit doesn't mean it is equal to it.

This is just plain wrong.

An infinite series is a sum of infinitely many terms. Such a sum can have a finite value, and if it has, it is said to converge.

Formally, if an infinite series is given with real (or complex) numbers a(n), we say that the series converges towards S or that its value is S if the limit
exists and is equal to S.

From here

 

[AznMaverick]

the limit of 0.999... IS 1. but if you take 0.9999... in a literal sense, they are NOT equal because just look at the two numbers they are obviously different. but if you look at them in a technical sense (with all the proofs, explanations, etc) they are equal...

 

[BigNeko]

.999...9 does not equal 1.

For
.999...9 + .000...1 = 1
let us agree that you can add as many 9s as you want to .999...9,
and that for every 9 you add, I will add a 0 to .000...1 (somewhere between the decimal and 1)
Then, this equation is ALWAYS true.
Since this equation is ALWAYS true, 1 does not equal .999...9


The shortest distance between two points is a straight line....

except for certain sub-atomic particles

 

[RossGr]

Originally posted by: MadRat
Funny how you say I have no need for mathematics. Quite the contrary. Math is important to my work, thank you very much.

I don't pity you because you believe .999...=1. Actually I pity you because you do not keep to the syntax of what you studied.

Must feel strange to use a tool which you do not understand, you must be some form of an engineer, or perhaps and even more likely an accountant, but then accountants don't really use math, aritimetic is not the sum total of math. Contrary to your statements I have stuck religiously to correct mathematical notation and syntax. It is you who on one hand calims we cannot deal with infinity and on the other speak of a "digit at infinity" . It is you who claims to have proven something in one sentence then in the next make provisions in case it is not true.

In the math I learned once something has been proven true it remains true.

I doubt that any true understanding of math is necessary for your job. If you use it you simply crank the handle of a machine and out pops an answer. You had better hope someone who understands the maching is on hand because the day may come when you crank the handle and out pops grarbage. Then you need to understand the workings of the machine. You do not.

 

[MadRat]

That last comment is so funny, Ross. You probably depend on the use of Enlish yet you have terrible writing skills. LOL

 

[MadRat]

Originally posted by: BigNeko
.999...9 does not equal 1.
For
.999...9 + .000...1 = 1
let us agree that you can add as many 9s as you want to .999...9,
and that for every 9 you add, I will add a 0 to .000...1

Actually, we don't need to depend on a number of 9's or 0's to determine the difference. The whole argument these guys have is that since you cannot halve the difference between 1 and .999... then there is no difference. The problem is that their rules, along with alot of common rules that apply to other numbers, do not work with infinity. We apply stipulations to the use of zero (the "null" value) yet they don't want to use the same intuition to apply relative counter stipulations to infinity.

 

[josphII]

Originally posted by: MadRat

Originally posted by: BigNeko
.999...9 does not equal 1.
For
.999...9 + .000...1 = 1
let us agree that you can add as many 9s as you want to .999...9,
and that for every 9 you add, I will add a 0 to .000...1

Actually, we don't need to depend on a number of 9's or 0's to determine the difference. The whole argument these guys have is that since you cannot halve the difference between 1 and .999... then there is no difference. The problem is that their rules, along with alot of common rules that apply to other numbers, do not work with infinity. We apply stipulations to the use of zero (the "null" value) yet they don't want to use the same intuition to apply relative counter stipulations to infinity.

that is not true at all! the proof begins with the number 0.999... and through the use of algebra and calculus it is shown to equal 1.

BigNeko,

there is a basic flaw with your reasoning that 0.999... + 0.000...1 = 1. the flaw is that 0.000...1 doesnt exist. you can not have an infinite string of 0's, and then have a number after that. infinity, by definition, has no end. so if your infinte string of 0's has no end, then how can a "1" come after it? it cant! this is a common mistake, and one that is easily shown to be flawed.

 

[josphII]

Originally posted by: AznMaverick
the limit of 0.999... IS 1. but if you take 0.9999... in a literal sense, they are NOT equal because just look at the two numbers they are obviously different. but if you look at them in a technical sense (with all the proofs, explanations, etc) they are equal...

why do people think that 0.999... has a limit? 0.999... is a number, nothing more. does the nubmer 2 have a limit? what about 3? what about pi? functions can have limits. series can have limits. but to say that a single number has a limit is just silly. yet another common mistake made by the people that think 0.999... != 1, and one that is easily shot down.

 

[josphII]

Originally posted by: MadRat

...The problem is that their rules, along with alot of common rules that apply to other numbers, do not work with infinity...

ok then please point out our error in the proof that 0.999... = 1

 

[RossGr]

Originally posted by: MadRat
That last comment is so funny, Ross. You probably depend on the use of Enlish yet you have terrible writing skills. LOL

I realize that , and have been crippled by it. Yet I struggle along. Difference is I recognize my short commings. You on the other hand are blind to yours.