Is 1 = 0.9999......

[VFAA]

Originally posted by: RossGr

Originally posted by: VFAA
Here's an example:

99.99% of the time 0.999 = 1.0

Hey, even 0.95 is rounded up to 1.0

100% wrong, .999 <> 1 never has been never will be.

I said rounded up to 1.0

I wish people could finally learn how to read English before taking math, though you really don't need to know English to know math

... But it helps to avoid confusion...

 

[TuxDave]

diieeeeeee..... everyone just dieeeeee..... anyways, I'm back.

Here's another question for those who took calculus. Taking the post from above.

lim 1/x = 0
x-> infinity

EQUALS ZERO.... infinity has that property where we don't have to write, "ehh.. it's a little bigger than 0... " Agree or disagree?

(btw.. I 100% believe 0.999... = 1)

 

[RossGr]

99.99% of the time 0.999 = 1.0

How many different ways can I read that statement?
Perhaps if you leaned how to be sarcastic in print it would have worked better.

 

[RossGr]

Originally posted by: TuxDave
diieeeeeee..... everyone just dieeeeee..... anyways, I'm back.

Here's another question for those who took calculus. Taking the post from above.

lim 1/x = 0
x-> infinity

EQUALS ZERO.... infinity has that property where we don't have to write, "ehh.. it's a little bigger than 0... " Agree or disagree?

(btw.. I 100% believe 0.999... = 1)

You can bet I agree with it.

 

[VFAA]

Originally posted by: RossGr

99.99% of the time 0.999 = 1.0

How many different ways can I read that statement?
Perhaps if you leaned how to be sarcastic in print it would have worked better.

Perhaps if you were smart enough you would've picked it up the 1st time...

I study Aviation. There's a lot of Math and Physics involved and in my field of study it really depends on what you're doing (solving for)... In most cases, .99s are rounded up to 1...

Here's something to think about... Is 0.999 = 1.0

 

[Skyclad1uhm1]

1 - 1/x = 0.999... for x = infinity, right?
(In the 10x calculation you use infinity for x too, so let's continue doing that)

1 - 1/infinity = 0.999...

Let's rewrite a bit:

1 - 0.999... = 1/infinity

'Multiply with infinity' (infinity is an abstract number anyway, not a concrete number):

infinity - (0.999...*infinity) = 1

If 0.999... = 1 you get infinity - infinity = 1


1 - 1 = 0

Multiply:

infinity - infinity = 0

If 0.999... = 1 you get 1 = 0
Works for me.

 

[RossGr]

This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

 

[Skyclad1uhm1]

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

 

[RossGr]

1 - 1/x = 0.999... for x = infinity, right?

Wrong, 1=.999....

.999.... + Anything > 1


Since your starting assumption is incorrect so are any results.

 

[VFAA]

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

hehe that was a trick question (0.999 = 1.0)... I'm glad competition is awake . Be surprised how many nuts do not know the difference ...

 

[RossGr]

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

College professor quoted where?

 

[RossGr]

Formal Proof of 1 =.999....

The math is pretty straight forward, there is a typo in the last equation of the first page and first equation of the second page, each of the sigmas should be multiplied by a 9.

This is one of the method used in Real analysis to prove such a fact.

one also needs to be aware of the definiton of eqality

x=y iff Abs(x-y) < d for all d>0 in the Set of Real numbers.

Proof,
if x = y , Abs(x-y)=0 , 0< d for all d>0 in the reals so the first half is easy

if abs(x-y) < d for all d> 0 in the reals then x=y
proof
assume x<>y

therefore either x>y or x<y

Case 1. x>y
if x>y then there exists some real number e>0 such that abs(x-y) = e

now if I choose a d = e/2 I have

abs(x-y) = e > e/2 =d so I have

abs(x-y)> d but this violates our given conditon abs(x-y)< d for all d in the reals This is a condratiction therefor our initial assumption is false, x>y cannot be true.

Case 2
x<y

Using the exact same logic as above I can establish a contradiction

since x>y cannot be true and x<y cannot be true it must be that x=y
QED

I have just shared with you a rather simple formal proof of the definition of equality.

Now if you do not agree with this definition you will need to provide a similar definiton so that we know what YOU mean when you say x=y

I have told you what I mean by this statement so there can be no confusion.

 

[VFAA]

RossGr you talking to me or the other guy?

I just brought a little sarcasm into the thread... didn't wanna let you have all the fun with numbers!

 

[RossGr]

Actually that is not pointed at any body. I just wanted to post some general information, seems like every body has there own idea at what equality means. I am trying to make it clear what I mean when I use the term.

any contributions of humor are appriciated.

 

[VFAA]

Originally posted by: RossGr
Actually that is not pointed at any body. I just wanted to post some general information, seems like every body has there own idea at what equality means. I am trying to make it clear what I mean when I use the term.

any contributions of humor are appriciated.

oh, OK

 

[Skyclad1uhm1]

Originally posted by: RossGr

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

College professor quoted where?

Check my post on Hackenstrings.

Edit: I agree with 0.999... = 1 in most circumstances, but not with just bringing infinity into a calculation about Real numbers to prove something. Infinity is not a number you can work with the same way you do with ordinary numbers, 10 * 0.999... - 0.999... does not give 9 just like that. That is like saying infinity - 1,000,000 = infinity, infinity - infinity = 0, give me $1,000,000 and you lose nothing!

 

[RossGr]

Check my post on Hackenstrings.

Oh that one, Ok,

If you will look at my proof you will see that I very carefully avoid any such operations.

the "proof" by adding 1/3 and .333.... or the algebraic manipulation "proof" are NOT proofs, they are demonstrations. While they do not constitute a vaild proof for the very reason you mention the result is correct. That can be proven correctly, has I have demonstrated in my link.

That link can be combined with the above definiton of equality to see that the result is mathematically correct.

 

[MadRat]

Originally posted by: silverpig
I did it with limits to show what answer you get...

note: infinity/infinity is actually an indeterminate form, but seeing as how it's y/y, you can say it is 1.

But it is not y/y.

 

[MadRat]

Originally posted by: RossGr
Madrat, your have referred to me editing things several times, not sure what you are talking about, If I make a content change I mark it as an edit, If I correct a typo (who?? Me, I never make typos! LOL) the edit will be within minutes of the original post and may not be noted.

RossGr, do you suffer paranoia?

 

[MadRat]

If you want to think of infinity then use base of infinity to determine the equivalent of .999... and you can deal with that undefined remainder. Just because the remainder is undefined in base 10 doesn't mean it has to remain undefined in other numbering systems.

x = (y - 1) / y
Solve for "x", where "y" = infinite.

These two pieces I've long since pointed out fit nicely together to destroy your logic of using a limit to solve for infinity. Rather than solve them you went back to limiting infinity. Infinity doesn't equal any number between 1 and itself, it equals itself. If you stick to the logic then you will find that the answer for x is .999..., which is .000...r1 away from 1.

The simplicity of this equation is throwing you guys for a loop, isn't it? You still are looking for a limit when this does not call for a limit.

Ross, your argumentum ad hominem attacks are a pretty weak attempt at recovery. For such a chronologically mature guy you sure have alot of room left for affective maturity.

 

[josphII]

x is .999..., which is .000...r1 away from 1

there is no such thing as 0.000...r1. how can you have an infinite number of zero's, and then a number after that? there is nothing after infinity, by definition

 

[RossGr]

Fine Madrat,
why do you not address my proof?

It still stands, it does not commit any of the crimes you complain about. How is it that an infinite number of digits can be contained in an infintly small box? Why? because that infinite string of digits represents a single point on the number line. It just happens to be the same location we call 1.

Not only does .999.... =1 but I can generate and infinite number of infinite series which all equal 1 and each is different.

sum (a /(a+1)^n) =1
n = 1 ->infinity

let a be any integer.


Damn that is a lot of different ways of writing one. Open your mind man! do not limit your self to a single representation of 1 or any other integer for that matter

 

[Budmantom]

I would say it's less then 1 but not by much.

 

[ElFenix]

you know, deep down in your soul, that pound of bricks is just a tiny bit heavier than that pound of feathers

 

[element]

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

College professor quoted where?

Check my post on Hackenstrings.

Edit: I agree with 0.999... = 1 in most circumstances, but not with just bringing infinity into a calculation about Real numbers to prove something. Infinity is not a number you can work with the same way you do with ordinary numbers, 10 * 0.999... - 0.999... does not give 9 just like that. That is like saying infinity - 1,000,000 = infinity, infinity - infinity = 0, give me $1,000,000 and you lose nothing!

You are mistaken. If I have an infinite number of dollars, and I give you $1,000,000 I DO lose nothing! The fallacy here is that I cannot ever have an infinite number of dollars, but the math still holds. Infinity can be used as a number of sorts. Infinity - $1,000,000 does equal infinity. And infinity-infinity does=0.

and 0.9999... does =1 !!!

I say again, you naysayers need to find a number between 1 and 0.999...
Stop trying to evade the question. You cannot find a number between 1 and 0.999... because it would be 0.0000 (infinite zeros go here) 0000001 but you can never write that last 1 !!!! you have to keep writing zeroes! so 1-0.99999...=0.0000000

Therefore 1=0.9999...