Is 1 = 0.9999......

[imported_Tomato]

Is 1 = 0.9999......

Yes, but I prefer writing it out as "1". Makes life easier.

Peace,
Dezign

 

[FrustratedUser]

I like my steaks medium rare.

 

[udonoogen]

Originally posted by: FrustratedUser
I like my steaks medium rare.

me too.

 

[silverpig]

Originally posted by: MadRat


What is the positional value of the lowest position in your .999...? If you dare say its "-infinity" then you just confirmed the existense of an infinite position. C'mon, you can do it. Its pathetic that you cannot simply admit that you are using infinity as the positional limit of your 9's. To say that there is no end to the nines only confirms that you are using infinity.

He is saying there are an infinite number of nines, but you cannot say that any particular nine occupies the "infinitieth" position.

Originally posted by: MadRat

The integer is a "1", as I've repeatedly said. Lets see, your question asked something it answered...

The integer is not a 1 or else you'd have 0.1. He is asking what position is the 1 in? Remember place value from elementary arithmetic? You know, the tenths spot, the hundredths spot... well what spot does the "1" occupy?

Originally posted by: MadRat

I do say it is at N with N being equal to -infinity, just as you'd need to define the infinitely placed last "9" in the .999...! LOL. You just don't get it that you're either going to prove we're both right or neither theory is right. You cannot have a truth that fails this simple litmus test of validity.

So if there is a 1 somewhere in your number, what comes after it? In an infinite string there is ALWAYS something after any particular number.

 

[silverpig]

Here is a link from another thread that seems to parallel half of the posts in this thread...

 

[RossGr]

Madrat,
I must admit I had no idea what you were attempting to say. It made no sence and still makes no sence.

Please do the construction with infinity as your number base. I do not believe it is possible because a number base, by defiition is an integer. Infinty is not a valid integer.

Likewise, there is no lowest postition value in .999... I make no effort to specfiy one, other then it is greater then N where N is any integer. I can associate an integer with every 9, you cannot say the same about your 1 at the infinite position. No, the postion value of your 1 (the one at infinity) is not 1, that location is occupied by a 0 (0* 10 ^-1). You cannot specify a postion for your 1, it MUST have an integer associated with it. How many times must I repeate this basic rule for you to actually read it.

You did not give a valid answer to the question last time, thereby proving my point that your 1 at the "infiite postition" does not and cannot exist. To say the position value of the the digit at infinity is infinity is circular reasoning which holds no water, anywhere.

For Nth time Every digit in a Real number MUST have a VALID integer assigned to it. If you cannot assign a valid integer to each digit it is NOT a REAL NUMBER. The basic process is called counting, something that is taught in kindergarden, it is not clear that you understand the concept. According to your methods you would count 1,2,3... infinity, and then must be done. The way I count it is 1,2,3,.....N, N+1, N+2,... I never reach any digit called infinity there is always a next integer. NOt only do YOU get to infinity YOU claim to be able to count infinity + 1, this is nonsence, infinity is not a number, by its very nature it corresponds to NO integer. Buzz Lightyear must be your idol..."To Infinity And beyond!" Sorry to me it just a cartoon, not something to base mathematics on.

 

[RossGr]

You also have this incessant need to use general rules that apply to Real numbers for infinity, in the case of finding the difference from 1 and .999... numbers

I am not sure what this means.

Are you saying that there is a flaw with writitng

.999.... = .9 + .0999...

Why is that not a completely valid statement, note that both sides of the eqation have a infinite tail, I do NO operation that effects any digit beyone the 1st. I do not bump anything off to infinity, waiting for it to vanish, in fact I do NOTHING with infinity, other then to carry it along.
I find it intesting that you who claims to be able to place digits at infinity and beyond have troubles and claim foul simply because I attempt to represent an infinite string of nines. At least I am consistent, You are not.
am I allowed to write

.99 = .9 +.09 ?

What is the difference? the .09 has an infite tail of 0s which I do not bother to represent, but they are there.

Please be very specific, so far you keep alluding to some error with the infinity, I want to know exactly what the errror is.

 

[MadRat]

Originally posted by: RossGr

Likewise, there is no lowest postition value in .999... I make no effort to specfiy one, other then it is greater then N where N is any integer. I can associate an integer with every 9, you cannot say the same about your 1 at the infinite position. No, the postion value of your 1 (the one at infinity) is not 1, that location is occupied by a 0 (0* 10 ^-1). You cannot specify a postion for your 1, it MUST have an integer associated with it. How many times must I repeate this basic rule for you to actually read it.

The limit of the 9's is at infinity. This is unquestionably the limit of the position.

Originally posted by: RossGr

You did not give a valid answer to the question last time, thereby proving my point that your 1 at the "infiite postition" does not and cannot exist. To say the position value of the the digit at infinity is infinity is circular reasoning which holds no water, anywhere.

Not only have I previously given you a valid expression of the infinite position, I've also shown how to display .999... using a base numbering system based on infinity.

Originally posted by: RossGr

For Nth time Every digit in a Real number MUST have a VALID integer assigned to it. If you cannot assign a valid integer to each digit it is NOT a REAL NUMBER. The basic process is called counting, something that is taught in kindergarden, it is not clear that you understand the concept. According to your methods you would count 1,2,3... infinity, and then must be done. The way I count it is 1,2,3,.....N, N+1, N+2,... I never reach any digit called infinity there is always a next integer. NOt only do YOU get to infinity YOU claim to be able to count infinity + 1, this is nonsence, infinity is not a number, by its very nature it corresponds to NO integer.

You've missed the whole concept of infinity if that is the definition you've chosen. Deductive reasoning with that definition would lend one to dismiss .999... as a Real number. Since you cannot count the 9's then it must not exist on the number line.

Originally posted by: RossGr

Buzz Lightyear must be your idol..."To Infinity And beyond!" Sorry to me it just a cartoon, not something to base mathematics on.

So funny I forgot to laugh. If you want a battle of wits you'd best remind yourself never come back empty handed.

 

[MadRat]

Originally posted by: RossGr

Are you saying that there is a flaw with writitng

.999.... = .9 + .0999...

Why is that not a completely valid statement, note that both sides of the eqation have a infinite tail, I do NO operation that effects any digit beyone the 1st. I do not bump anything off to infinity, waiting for it to vanish, in fact I do NOTHING with infinity, other then to carry it along.

The difference is that your operation happens at the 10^-1 position, not at an infinite position, therefore you do not violate any logical conventions with this operation. This doesn't have anything to do with your argument.

 

[silverpig]

There is no "limit of 9s". That's the idea of them being infinite, there is no end (limit) to them.

The limit of a SUM however, is an entirely different concept from the flawed one you are trying to get across here.

 

[Yomicron]

Originally posted by: MadRat

Originally posted by: RossGr

For Nth time Every digit in a Real number MUST have a VALID integer assigned to it. If you cannot assign a valid integer to each digit it is NOT a REAL NUMBER. The basic process is called counting, something that is taught in kindergarden, it is not clear that you understand the concept. According to your methods you would count 1,2,3... infinity, and then must be done. The way I count it is 1,2,3,.....N, N+1, N+2,... I never reach any digit called infinity there is always a next integer. NOt only do YOU get to infinity YOU claim to be able to count infinity + 1, this is nonsence, infinity is not a number, by its very nature it corresponds to NO integer.

You've missed the whole concept of infinity if that is the definition you've chosen. Deductive reasoning with that definition would lend one to dismiss .999... as a Real number. Since you cannot count the 9's then it must not exist on the number line.

so if you can not count all the digits then it is not a number? so pi isn't a number? sqrt(2) isn't a number?

I can't count all the digits in 1.000... so it isn't a number either.


1.000... = 0.999...

 

[MadRat]

Infinity has never meant unlimited except when used in Latin. Infinity in modern language simply implies an indeterminate number.

If we do take your "unlimited" defintion then you make .999... into a number outside the Real numbers. Why? Because the meaning of .999... is immeasurable IF the position has no definitive limit. You may theorize that all positions in the sequence will be 9's, but can you write out the number to prove it? No. Without a way to prove the concept it must be judged as invalid.

I think you soothsayers should take a dose of your own medicine and realize the .999...=1 argument is futile.

 

[RossGr]

Not only have I previously given you a valid expression of the infinite position, I've also shown how to display .999... using a base numbering system based on infinity.

You have? when? where? You speak of it but I have not seen any construction.

You've missed the whole concept of infinity if that is the definition you've chosen. Deductive reasoning with that definition would lend one to dismiss .999... as a Real number. Since you cannot count the 9's then it must not exist on the number line.

Still wrong, there is no end to the integers, I can assign every 9 an integer, simply by counting, by ones, or twos, or millions or hundreds of millions. A nine for every integer, and integer for every nine each is specified. I NEVER arrive at some integer called infinity, it does not exist.

The difference is that your operation happens at the 10^-1 position, not at an infinite position, therefore you do not violate any logical conventions with this operation. This doesn't have anything to do with your argument.

Just goes to show that you either did not read or could not understand the proof. That is only operation I did. I DO NOT DO ANY OPERATION ON A DIGIT AT INFINITY. Is it somehow not true that .9...9 + .0...0999... Where the ellipsis in the middle represents the ommission of the SAME FINITE number of digits is not true? The only statement I make about .0...0999... is that it is greater then zero. Do you claim that to be false? Perhaps you ought to do yourself, and all of us, a favor and actually go back and examine the Proof.

 

[RossGr]

Originally posted by: MadRat
Infinity has never meant unlimited except when used in Latin. Infinity in modern language simply implies an indeterminate number.

If we do take your "unlimited" defintion then you make .999... into a number outside the Real numbers. Why? Because the meaning of .999... is immeasurable IF the position has no definitive limit. You may theorize that all positions in the sequence will be 9's, but can you write out the number to prove it? No. Without a way to prove the concept it must be judged as invalid.

I think you soothsayers should take a dose of your own medicine and realize the .999...=1 argument is futile.

Just how do you think infinity is defined in the extension of the real number system?

The starting point is

Let I= infinity (Generally the sideways 8 is used, can't do that here)

I > x for all x in the Real Numbers

-I < x for all x in the Real Numbers

I + x = I for all x in the Real Numbers

etc.

I am forced to work with this definition if I am dealing with the real number system.

What is your definition of infinity?

 

[BigNeko]

Well,
welcome to the flame fest. I sense that some folks are getting uncomfortable with this, but they can always go elsewhere.

MadRat, RossGR was being reasonable, and he is at least trying to show us why he thinks he is right. Since he is one of maybe two here doing this, cut him slack and stay on topic.

As to Exhibit A, Galileo must have been a moron also. Cool

RossGR, after some short research I have this question.
Is infinity a subset of infinity plus one?
Is infinity plus one a subset of infinity?

Is the math you are sing based on set theory?

Gotta catch my flight, will catch up later.

 

[jman19]

Neko,

I'm pretty sure that, by definition, inf + 1 = inf, so to ask if inf is a subset of inf+1 is pointless...

 

[RossGr]

BigNeko,
Let us put your question into the context of real numbers. First we need to look at the partial definition of infinity I posted just above. The most remarkable thing about this definition is that it does not define what infinity is but what it is NOT.

I>x for All x in the Reals

This says that if x is a Real number it is LESS THEN infinity. How do we capture this definition in a set? Not clear to me.

Now if we do suceed in defining the set {infinity} what does {infinity +1} mean, by my definition of infinity above

I + x = I for all x in the Real numbers

We would have to write {Infinity +1 } = {Infinity} since every set contains itself as a subset then the answer to your question would be yes, but it is still not clear to me just what {Infinity} consists of.

And, yes Real Analysis is most definitly based on set theory.

Did this help? or Only confuse?

 

[CallTheFBI]

Originally posted by: spidey07
Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

You would think that guy would be smart enough to can that messed up method he uses to put equations on his web site and use an equation editor in Word Perfect or Microsoft Word.

 

[MadRat]

Originally posted by: RossGr

You've missed the whole concept of infinity if that is the definition you've chosen. Deductive reasoning with that definition would lend one to dismiss .999... as a Real number. Since you cannot count the 9's then it must not exist on the number line.

Still wrong, there is no end to the integers, I can assign every 9 an integer, simply by counting, by ones, or twos, or millions or hundreds of millions. A nine for every integer, and integer for every nine each is specified. I NEVER arrive at some integer called infinity, it does not exist.

Originally posted by: RossGr
Just goes to show that you either did not read or could not understand the proof. That is only operation I did. I DO NOT DO ANY OPERATION ON A DIGIT AT INFINITY. Is it somehow not true that .9...9 + .0...0999... Where the ellipsis in the middle represents the ommission of the SAME FINITE number of digits is not true? The only statement I make about .0...0999... is that it is greater then zero. Do you claim that to be false? Perhaps you ought to do yourself, and all of us, a favor and actually go back and examine the Proof.

There is no position for the tail by your definition of infinite, therefore you cannot assign an "unlimited" number a nines any value. Your logic is completely missing here because again you are comparing unlike quantities. The only person comparing .9999 with .999... is you, by trying to prove 9's exist at every position of .999... when in your definition there is no limit. All metrics must be fit within limits. Infinity is a valid positional limit as long as your operations do not affect that position. Infinite in that case means that it is an indeterminate location, not that it is sitting in some finite position.

You are still trying to show a relationship between .999... and 1, in order to show that no difference exists. Awww, you are going to say there is no subtraction. But to prove your point you chose to rewrite the equation so that it appears to add instead. It is written as a comparison which can be rewritten as an equation in simplest terms, an equation that will include subtraction. You also choose to use it in such a way that you perverse the use of infinite series. Ommission of the limit to your nines, in your proof, at infinity does not mean the limit at the infinite position doesn't exist. That just means by your definition .999... is not a Real number.

Originally posted by: RossGr

I am forced to work with this definition if I am dealing with the real number system.

And forced there because the limits of your equation are at an infinite position.

Originally posted by: BigNeko
Well,
welcome to the flame fest. I sense that some folks are getting uncomfortable with this, but they can always go elsewhere.
MadRat, RossGR was being reasonable, and he is at least trying to show us why he thinks he is right. Since he is one of maybe two here doing this, cut him slack and stay on topic.
As to Exhibit A, Galileo must have been a moron also. Cool

BigNeko, the flames have rolled off his fingertips since his first post here. Please don't feed the troll by mentioning Galileo in the same post as him else he might feel equal to him. I'd cut him some slack if he would stay within the premises of logic. I can tolerate his spelling. I can tolerate his little childish insults. That is more than he deserves and he won't be getting any more slack than that.

 

[Kyteland]

Originally posted by: bleeb

By stating the fact that the people who say that 0.9999 != 1 are "ignorant masses" no doubt labels you as a "close-minded bastard". Please try to keep this reasonable please. What the "masses" believed at the time was dependent on the available technology and relative state of knowledge. The world was flat to people because they were immersed in it. They weren't able to determine it otherwise...

And the statement regarding the cheese. I'm not sure if people actually believed the moon was made of cheese, but there was a greater point that I was trying to make. And that point was to show that the people believed in one thing because they were limited by the current state of knowledge. This might be the case now with you.

0.9999.... != 1

Q.E.D.

bleeb, let me paraphrase the above post for the benefit of this discussion.

"... the people who say that 0.9999 != 1 are "ignorant masses" ... They weren't able to determine it otherwise... And ... I'm not sure if ... 0.9999.... != 1"

Form this it is quite obvious that 0.999...=1 . All further arguments are baseless.

 

[RossGr]

All metrics must be fit within limits. Infinity is a valid positional limit as long as your operations do not affect that position. Infinite in that case means that it is an indeterminate location, not that it is sitting in some finite position.

Using some big words there to bad you have no clue as to what you are saying. Do you know what a metric is? What is the limit on the R1 metric or the R2? How is infinity a valid positional limit, what does that mean? What is the integer at the infinite position? Is this something that exists indepentent of the integers? What number system are you using?

All I get from your posts are questions. They do not contain any mathematics that I have ever seen, where did you get these ideas? Did you ever learn to count?


So

There is no position for the tail by your definition of infinite, therefore you cannot assign an "unlimited" number a nines any value.

What? By my definition of infinite the tail starts at some integer, N, feel free to choose any, and continues from there for N+1, N+2 and so forth for eacn integer, remember kindergarden and counting? I there some trouble with this? Where is the operation that effects the "infinite postition" . I am getting tired of repeating this, I do no operation at infinity I do all of my operations on integer values, that is all there is can do nothing else.

You literary definiton of infinity has no use here, it is every bit as out of place in this discussion as if I were to transport my Mathematical definitions in to a dicussion of the supernatural.

Why can't I assign an unlimited number of 9s a value? You provid no reasoning as to why you simply state that it cannot be. I show with simple operations that Abs(1 - .999....) < 10^-N for all integers, None of these operations involve arithemitc at infinity. I use the symbol .999.... as a symbol only, I make no assumption other then it is greater then 0 I do not claim that it is less then anything I only claim greater then. You are going to have to keep trying to point out an error. You have not countered my argument yet. YOU claim opertationsat infinity that do not happen, YOU seem to be claiming that .999.... is some how infinite, does thing mean that you belive that .999... is greater then 1? Please provide some form of clear statement of how this could be true. IF it is not greated then one then what does this

therefore you cannot assign an "unlimited" number a nines any value.

mean?

Awww, you are going to say there is no subtraction.

What does that mean? Since you are the expert language critic I must take it literelally. You seem to be the one haveing trouble with subtraction and other basic arithmitic, Will you please point out the illegal operation in my proof. Make a effort to raise a valid point, so far you have not.

 

[MadRat]

Originally posted by: RossGr

All I get from your posts are questions. They do not contain any mathematics that I have ever seen, where did you get these ideas? Did you ever learn to count?

Go figure. I'm glad you are thinking about what I say and now have questions. Too bad you haven't grasped the concept of infinity.

 

[GermyBoy]

You are all stupid. No, it doesn't. It is fact.

Infinity cannot be reached ever.

God does not exist.

All facts.

 

[silverpig]

Originally posted by: GermyBoy
You are all stupid. No, it doesn't. It is fact.

Infinity cannot be reached ever.

God does not exist.

All facts.

Care to read the thread or any of the numerous proofs? No one is trying to reach infinity here.

MadRat: You keep posting "You cannot do that," "that is invalid," "you must do it this way," etc, yet you do not show what you can do, what is valid instead, or how you must treat things. You spout things off in english, but you have not demonstrated anything mathematically.

 

[bleeb]

Originally posted by: silverpig

Originally posted by: GermyBoy
You are all stupid. No, it doesn't. It is fact.

Infinity cannot be reached ever.

God does not exist.

All facts.

Care to read the thread or any of the numerous proofs? No one is trying to reach infinity here.

MadRat: You keep posting "You cannot do that," "that is invalid," "you must do it this way," etc, yet you do not show what you can do, what is valid instead, or how you must treat things. You spout things off in english, but you have not demonstrated anything mathematically.

we're just having fun with mathematics.. but there are a few who are just so closeminded its appalling