Thread: Does 0.9 repeated = 1?

Originally Posted by A Roxxor

There are an infinite amount of numbers between any two given numbers.

Perhaps that is not always true.

Devil's advocate there. I am convinced that 1 = 0.999..., and my part in this thread isn't about whether or not the two figures are equal. I am just saying that it is a paradox that has not been completely explained.

Originally Posted by A Roxxor

Yes it does.

In order to get 1 from .9... You have to add .0...1 to it, i.e. Zero. Therefore, they are the same number.

What is 0.00000...1? The figure suggests that there is something on the other side of infinity. Does it not? It definitely suggests that there is something, which is not nothing. That is part of the paradox. Yes, your math is accurate, but notice the paradox.

Originally Posted by A Roxxor

No.

There is nothing on the other side of infinity, or anyhting like that, .9... is just an alternate way of writing 1.

You are just reasserting your conclusion and not dissecting the paradox. I am calling into question certain aspects of the fact that the two figures are equal, not asking you to state again that they are equal. Telling me that one is a way of writing the other adds nothing to your conversation with me except a reassertion of the fact that I am trying to dissect.

Originally Posted by A Roxxor

Your analogy isn't valid because there is no border at all. A shared side is a border.

The border has no width, yet it is a border. The border between the rectangles is just as wide as the border between 0.999... and 1?

Devil's advocate again.

Originally Posted by A Roxxor

What paradox?

You are now officially on my troll watch list.

Just in case you or somebody else STILL doesn't get the paradox, I will explain it another way. And I am not calling into question whether the two figures are equal, so don't waste your time by telling me they are just two ways of writing the same number. That fact is exactly what I am trying to explain, not counter. Understand?

Okay, imagine the number 0.999... written on a piece of paper that goes forever. With every next digit, the number represented up to that digit is a little closer to 1. So how far along the number is there a point when the digits up to that point equal 1? A trillion light years? Quadrillion to the octillionth power light years? It never happens, ever, obviously. Infinity has no end. So the number can never reach 1, ever. Right? So the stretched out number that never can possibly get to 1 gets to 1 because that is the number that the entire number is. It can't reach 1, but it reaches 1.

Considering the very specific issue I have raised, why are the two figures representative of the same number, which they are? And please don't tell me what a converging geometric series is. That is the very thing I am calling into question.

It will never reach 1 if you try to write it out on paper because you will always end up writing a finite number of 9s. But 0.999~ does not represent a finite number of 9s, it represents an infinite number of 9s.

Perhaps that is not always true.

If you have any two real numbers which are not equal, then yes, there will be an infinite number of reals between those two numbers. You can't even count them (I can demonstrate if you want, it's quite interesting; there are infinity natural numbers, but there is an even greater infinity of real numbers).

Originally Posted by Xei

It will never reach 1 if you try to write it out on paper because you will always end up writing a finite number of 9s. But 0.999~ does not represent a finite number of 9s, it represents an infinite number of 9s.

If you have any two real numbers which are not equal, then yes, there will be an infinite number of reals between those two numbers. You can't even count them (I can demonstrate if you want, it's quite interesting; there are infinity natural numbers, but there is an even greater infinity of real numbers).

is there such a thing as infinity plus 1? if there is no such thing, then there are no numbers inbetween 0.9 recurring and 1.

what exactly are the numbers inbetween 0.9 recurring and 1? just name one for me. keeps in mind that infinity plus something probably doesnt exist, so dont say something like, 0.(9*infinity + 1)

That's the point. They are the same number because there are no numbers inbetween.

Originally Posted by Kushna Mufeed

That's the point. They are the same number because there are no numbers inbetween.

thats not the reason why i think 0.9 rec. = 1, i was just explaining that there are no numbers inbetween. i think this has nothing to do with it. but i explained in a few posts ago why it must be.

Originally Posted by Xei

It will never reach 1 if you try to write it out on paper because you will always end up writing a finite number of 9s. But 0.999~ does not represent a finite number of 9s, it represents an infinite number of 9s.

Can infinity be reached?

The 9's on the piece of paper never get to a point where the number has a value of 1, yet they do.

Originally Posted by Xei

If you have any two real numbers which are not equal, then yes, there will be an infinite number of reals between those two numbers. You can't even count them (I can demonstrate if you want, it's quite interesting; there are infinity natural numbers, but there is an even greater infinity of real numbers).

At least in every case you know of.

Originally Posted by slash112

is there such a thing as infinity plus 1?

No. So, is there such thing as 0.000...1?

Originally Posted by Universal Mind

No. So, is there such thing as 0.000...1?

i dont see what that has to do with it, but it doesnt matter anyway because i was just clearing up the fact that it is possible to have no numbers inbetween two numbers.

Originally Posted by slash112

i dont see what that has to do with it, but it doesnt matter anyway because i was just clearing up the fact that it is possible to have no numbers inbetween two numbers.

Somebody else was talking about 0.000...1, and I asked you if such a number is possible because you said there is no such thing as a step past infinity. I was trying to bring you into that subdiscussion, and anybody else who might want to take a stab at it.

Originally Posted by Universal Mind

Somebody else was talking about 0.000...1, and I asked you if such a number is possible because you said there is no such thing as a step past infinity. I was trying to bring you into that subdiscussion, and anybody else who might want to take a stab at it.

you know something, i never thought about it, and i never realsed someone brought it up, this brings a whole other side to the arguement. let me think about it for a while, i would instictivly say yes it is possible, but i need to think logically...

Originally Posted by Universal Mind

The 9's on the piece of paper never get to a point where the number has a value of 1, yet they do.

At least part of the paradox is probably saying never when talking about infinity. By definition, the end of infinity is "never".

Er.. my head hurts now.

By the way, I don't thing that rectangles analogy is really applicable, since a real number has no width. More like two lines sharing a side.

Originally Posted by RedfishBluefish

At least part of the paradox is probably saying never when talking about infinity. By definition, the end of infinity is "never".

But when it is also an "ever", it is paradoxical.

Originally Posted by RedfishBluefish

By the way, I don't thing that rectangles analogy is really applicable, since a real number has no width. More like two lines sharing a side.

Good point. But, uh, how can I rationalize against that? Then why is it that a 10 foot wide wall is so much wider than a 1 foot wide wall?

Okay, I am going to stop playing devil's advocate right about now. I don't like arguing stuff I don't agree with. That is why I don't practice law.

i dont really want to believe that the two numbers are the same, but you cant argue with the proof. e.g. the thing i said earlier, about 1/9 = 0.1 rec. * 9 = 0.9 rec. and 1/9 * 9 = 9/9 even thouh 9/9 = 1 usually, so it equals two things. so they must be the same.

Originally Posted by Universal Mind

Perhaps that is not always true.

It is.

Devil's advocate there. I am convinced that 1 = 0.999..., and my part in this thread isn't about whether or not the two figures are equal. I am just saying that it is a paradox that has not been completely explained.

But it isn't a paradox. It's just an alternate way of writing '1'. They are equal, and you can use them interchangeably.

What is 0.00000...1? The figure suggests that there is something on the other side of infinity. Does it not? It definitely suggests that there is something, which is not nothing. That is part of the paradox. Yes, your math is accurate, but notice the paradox.

It's a reversed pattern of 0.10... It means infinite amount of zeros and then a '1'. Which makes it zero BECAUSE there is nothing on the other side of infinity.

You are just reasserting your conclusion and not dissecting the paradox. I am calling into question certain aspects of the fact that the two figures are equal, not asking you to state again that they are equal. Telling me that one is a way of writing the other adds nothing to your conversation with me except a reassertion of the fact that I am trying to dissect.

Then you might as well dissect why the numbers .5 and 1/2 are the same number.

You can't give me any explanation other than they are interchangable and their values are equal, and then I could go on to say that there must then be some mystical 'other kind' of number that determines true value, right?

Well, no. There isn't. They're the same because they are equivalent. They are two representations of the same value, that is it.

The border has no width, yet it is a border. The border between the rectangles is just as wide as the border between 0.999... and 1?

Devil's advocate again.

No, there is no border. They aren't two rectangles sharing a side, they're a rectangle that's been labelled twice.

You are now officially on my troll watch list.

Just in case you or somebody else STILL doesn't get the paradox, I will explain it another way. And I am not calling into question whether the two figures are equal, so don't waste your time by telling me they are just two ways of writing the same number. That fact is exactly what I am trying to explain, not counter. Understand?

No, because this is math and ultimate truth in it is represented by using itself to demonstrate that something works.

As long as you can show that x = y, then it is true. There is nothing else here to look at.

Okay, imagine the number 0.999... written on a piece of paper that goes forever. With every next digit, the number represented up to that digit is a little closer to 1. So how far along the number is there a point when the digits up to that point equal 1? A trillion light years? Quadrillion to the octillionth power light years? It never happens, ever, obviously.

Exactly. They aren't they same way of writing the number, obviously. They both represent the same value. 0.9... Will never 'become' 1, but it is of the same value as 1, because that's how maths works.

Infinity has no end. So the number can never reach 1, ever. Right? So the stretched out number that never can possibly get to 1 gets to 1 because that is the number that the entire number is. It can't reach 1, but it reaches 1.

Considering the very specific issue I have raised, why are the two figures representative of the same number, which they are? And please don't tell me what a converging geometric series is. That is the very thing I am calling into question.

You aren't getting it.

.9... DOESN"T reach one. It isn't 1. It's .9... However, they both represent the same value.

This is the same reason that 1/2 never 'becomes' 2/4 or 2^-2 1/4.

They are the same, again, because:

1. there are no boundaries between the numbers on a number line
2. they represent the same value

Originally Posted by A Roxxor

But it isn't a paradox. It's just an alternate way of writing '1'. They are equal, and you can use them interchangeably.

Hey troll, you know I have addressed that about 10 times in this thread, unless you are not reading my posts. I addressed you specifically yesterday when I said I am trying to dissect your assertion and not counter it. Your response causes your argument to be circular. Look into it.

Originally Posted by A Roxxor

It's a reversed pattern of 0.10... It means infinite amount of zeros and then a '1'. Which makes it zero BECAUSE there is nothing on the other side of infinity.

The way the number is written suggests that there is something on the other side of infinity.

Originally Posted by A Roxxor

Then you might as well dissect why the numbers .5 and 1/2 are the same number.

Okay, you are definitely trolling. You are repeating Drew's argument that was already thoroughly covered. The rest of your post is about countering the claim that the two numbers are not equal, and I have thoroughly and repeatedly explained that I am not taking issue with the claim that the numbers are equal except to point out the paradoxical nature of the fact while agreeing that it is a fact. Please do something with your life. Thanks.

*Spews out Raspberry Tea from mouth* A Roxorr isn't banned?!? No offense, but I thought that you were...

Originally Posted by spockman

*Spews out Raspberry Tea from mouth* A Roxorr isn't banned?!? No offense, but I thought that you were...

His last incarnation was, and his new one probably will be any minute now.

I'm glad you finally admit it.

Admit what?

I said if you can't intuitively accept it then you'll just have to accept the proof.

I personally have no problem with it and see no paradox.

You just have to accept it, right? But I gave meaning to the exponent of 0. Is that what set off your asshole response? I knew it would be coming in right about the time you felt stumped. So predictable. Get help, seriously.

I'm trying have a reasoned discussion here. There was nothing remotely inflammatory about my response. Why are you responding like that?

First of all, 2^-1 is not paradoxical. It presents no apparent contradictions we can't explain away. What does it mean? It means 2 represented -1 times, which is 2 represented 1 time in reciprocal form. 2^-1 = 1/2. The negativity of exponents creates reciprocality due to the geometric aspect and not simple left movement on a number line, which is arithmetic.

Also, 2^-1 does not represent "multiply 2 by 2 -1 times". An exponent represents the number of times a number is represented, not how many times it is multiplied by itself. A number with an exponent of 1, for example, is represented 1 time, not multiplied by itself 1 time. A number with an exponent of 2 is multiplied by itself 1 time since it is represented 2 times.

Yes sorry I meant 2^3 means 2 multiplied by itself 3-1 times, etecetera.

How can you 'represent' a number a negative amount of times? There is very little intuitive meaning you can give to this.

2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
2^3 = 2 * 2 * 2
2^2 = 2 * 2
2^1 = 2

2^-1 = ?

The fact is negative numbers are just as 'unreal' as imaginary numbers. You can't physically represent a negative number of objects.

You need to give up on your desperate rationalization. It is dishonest and pathetic, along with being just really shitty.

What on Earth is wrong with you?

I wholeheartedly mean everything I say, otherwise I would not say it. You think I have some sort of agenda here?? My view also happens to agree with every piece of literature about the nature of mathematics I've ever read. I suggest you read some books about formal systems such as Godel Escher Bach or The Emperor's New Mind.

The real numbers are in fact real. The imaginary numbers are in fact imaginary. If real numbers are not real, why didn't they just make pi = 3? Humans invented the symbols but discovered the numbers. Math is completely logical, and we do not decide on its rules or its components, only its symbols.

Maths does not have monopoly on logic actually.

There are true statements about numbers which cannot be proved with maths.

The first thing you should have been taught when learning about IMAGINARY numbers is that IMAGINARY is a technical term, not the adjective imaginary. The nomenclature comes from an old prejudice against French mathematics. It is now completely redundant.

pi is something which results from Euclid's postulates. Euclid's postulates are a model, and are actually physically wrong to high degrees of precision. But using Euclid's postulates and calculus, we can calculate that the number pi is equal to

4/1 - 4/3 + 4/5 - 4/7...

This is the only value that pi can have. It is not arbitrarily defined.

... which makes it not real. The square root of -1 does not exist. However, you are looking at 1 post right now.

Yes, but I'm not looking at the number '1' right now, am I?

You are using '1' to describe objects in physical reality.

Equally I could describe various physical phenomena using i (and could not without).

I could also use 'quite long' to describe your post. This doesn't mean that 'quite long' exists.

A matrix is a human system for listing and working with numbers. They are not numbers themselves. They involve real operations, but they are not naturally existing operations in and of themselves.

1 and
10
01
are exactly the same thing. How can you claim that one way of representing it is real yet another is not? I can perform exactly the same operations upon it and get exactly the same answers.

I did not say real numbers have physical existence. I said they are real. Matter is not the only form of reality.

Okay, real numbers do not have physical existence. Neither do imaginary numbers. This is obvious. But this 'other reality' which you hint at; why does i not belong there whilst 1 does?

Originally Posted by Xei

2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
2^3 = 2 * 2 * 2
2^2 = 2 * 2
2^1 = 2

2^-1 = ?

ok, 2 to the power of -1 is 1/2, any idiot knows that.

and by the way, from a post you made earlier aswell, 2 to the power of 0 is 1. anything to the power of 0 is 1, any idiot knows that aswell.

Originally Posted by Xei

Admit what?

I said if you can't intuitively accept it then you'll just have to accept the proof.

I personally have no problem with it and see no paradox.

If you can't see the seeming contradiction intuitively, then you will just have to accept that there is one.

Originally Posted by Xei

I'm trying have a reasoned discussion here. There was nothing remotely inflammatory about my response. Why are you responding like that?

Uh, because you made the shit-head comment that I don't know much about math? If you aren't aware of the fact that your ignorant comment was a blatant personal insult, you have a world of social skills training to undergo.

Originally Posted by Xei

Yes sorry I meant 2^3 means 2 multiplied by itself 3-1 times, etecetera.

Very good.

Originally Posted by Xei

How can you 'represent' a number a negative amount of times? There is very little intuitive meaning you can give to this.

2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
2^3 = 2 * 2 * 2
2^2 = 2 * 2
2^1 = 2

2^-1 = ?

Its reciprocal. See my earlier post for the geometric change explanation.

Originally Posted by Xei

The fact is negative numbers are just as 'unreal' as imaginary numbers. You can't physically represent a negative number of objects.

There is a reason they are called real numbers. Do you think it is just some random word that was chosen? There are negative temperature degrees, you can owe negative amounts of money, and you can have negative amounts of money in an account. Negative numbers are real. But the square root of -1 flat out does not exist. It is only a hypothetical concept.

Originally Posted by Xei

What on Earth is wrong with you?

I don't respond very nicely to unnecessary assholishness. Please forgive yourself.

Originally Posted by Xei

I wholeheartedly mean everything I say, otherwise I would not say it. You think I have some sort of agenda here?? My view also happens to agree with every piece of literature about the nature of mathematics I've ever read. I suggest you read some books about formal systems such as Godel Escher Bach or The Emperor's New Mind.

I suggest you counter my arguments instead of appealing to Hofstadter and other eccentric writers.

Originally Posted by Xei

Maths does not have monopoly on logic actually.

No, but logic has a monopoly on math, actually.

Originally Posted by Xei

There are true statements about numbers which cannot be proved with maths.

Yes.

Originally Posted by Xei

The first thing you should have been taught when learning about IMAGINARY numbers is that IMAGINARY is a technical term, not the adjective imaginary. The nomenclature comes from an old prejudice against French mathematics. It is now completely redundant.

There is no square root of -1. Can you tell me what it is, aside from the letter i that is used to merely symbolize it? Can you tell me? You can't. That is why the word "imaginary" was used to describe the unit. There is no square root of a negative number.

Originally Posted by Xei

pi is something which results from Euclid's postulates. Euclid's postulates are a model, and are actually physically wrong to high degrees of precision. But using Euclid's postulates and calculus, we can calculate that the number pi is equal to

4/1 - 4/3 + 4/5 - 4/7...

This is the only value that pi can have. It is not arbitrarily defined.

Pi is something that results from the ratio of a circle's circumference to its diameter. Period. It is not some crazy number Euclid made up out of nowhere. It is REALITY. That is why we have to deal with the fact that the number is such a pain in the ass. We have no choice. Reality is what it is. Math is what it is. We only create the symbols.

Originally Posted by Xei

Yes, but I'm not looking at the number '1' right now, am I?

You are using '1' to describe objects in physical reality.

There is still 1 computer. That does not mean 1 is an object. Again, matter is not the only form of reality. 1 is a logical concept. The square root of -1 is an illogical concept.

Originally Posted by Xei

Equally I could describe various physical phenomena using i (and could not without).

Fill in the blank. One time, somebody had i ________.

Originally Posted by Xei

I could also use 'quite long' to describe your post. This doesn't mean that 'quite long' exists.

One is a vague description, and the other is an exact figure. However, if my post really is "quite long", then "quite long" exists.

Originally Posted by Xei

1 and
10
01
are exactly the same thing. How can you claim that one way of representing it is real yet another is not? I can perform exactly the same operations upon it and get exactly the same answers.

An operation you can do with the matrix gives the same figure. The matrix is a man made system of representing numbers, which existed long before we ever did.

Originally Posted by Xei

Okay, real numbers do not have physical existence. Neither do imaginary numbers. This is obvious. But this 'other reality' which you hint at; why does i not belong there whilst 1 does?

I will give you the answer again in i days.


The end of infinity is a paradox. I have yet to see a viable counterargument to that.

Originally Posted by Universal Mind

Hey troll, you know I have addressed that about 10 times in this thread, unless you are not reading my posts. I addressed you specifically yesterday when I said I am trying to dissect your assertion and not counter it. Your response causes your argument to be circular. Look into it.

No, it doesn't.

They are the same number becuase they have the same value and are in the same place on a number line.

Again, no borders. The rectangle has been labelled twice. There is nothing "on the other side" of infinity. You don't have an argument at all.

My argument isn't circular, anyway. Several proofs have been produced. They are the same. There's nothing to dissect, again. Do you even know what you're talking about?

Two numbers are the same number-- equal-- when they are on the same place on the number line. i.e. .9... and 1. There's nothing more to it.

All you've done is ask why they are. Look at the proofs. I know you aren't countering it. That's why I'm explaining it

You're pretty rude, btw. If you don't want an answer, then don't ask for one.

The way the number is written suggests that there is something on the other side of infinity.

No it doesn't...?

Infinity can never be "reached" because it is a concept of an unreachable number. Therefore the only thing that can be behind it is itself.

Okay, you are definitely trolling. You are repeating Drew's argument that was already thoroughly covered.

Quote, please? I haven't read most of this thread. Just your posts.

The rest of your post is about countering the claim that the two numbers are not equal, and I have thoroughly and repeatedly explained that I am not taking issue with the claim that the numbers are equal except to point out the paradoxical nature of the fact while agreeing that it is a fact.

But it isn't paradoxical.

You still aren't getting it. The only way to explain this is by demonstrating that it isn't, which is the same as demonstrating that they are the same.

Again, 1 and .9... are the same number. There isn't anything paradoxical about this because they occupy the same place on the number line.

Think aobut it this way.

.9... is the decimal form of the value '1' and '1' is the fractional form.

Paradox disappears pretty fast, right?

Please do something with your life. Thanks.

And what's with all the ad homeneim attacks?

Grow up, man.

Originally Posted by A Roxxor

They are the same number becuase they have the same value and are in the same place on a number line.

.9... is the decimal form of the value '1' and '1' is the fractional form.

Oh, what a very witty and clever way to dismiss my post. I wish I was as smart as you! :3

You still haven't explained this paradox, so obviously I can't explain much mor eto you...

All you've given me is that '.9... proves there is something beyond infinity' which is nonsensical.

You haven't explained how that is. .9... is a number. Infinity is never reached, and definitely not passed...

So, what the hell are you talking about?

I am sure you missed it when I addressed you specifically with this one of my many explanations of my point, troll.

Originally Posted by Universal Mind

Just in case you or somebody else STILL doesn't get the paradox, I will explain it another way. And I am not calling into question whether the two figures are equal, so don't waste your time by telling me they are just two ways of writing the same number. That fact is exactly what I am trying to explain, not counter. Understand?

Okay, imagine the number 0.999... written on a piece of paper that goes forever. With every next digit, the number represented up to that digit is a little closer to 1. So how far along the number is there a point when the digits up to that point equal 1? A trillion light years? Quadrillion to the octillionth power light years? It never happens, ever, obviously. Infinity has no end. So the number can never reach 1, ever. Right? So the stretched out number that never can possibly get to 1 gets to 1 because that is the number that the entire number is. It can't reach 1, but it reaches 1.

Okay...

That's not a paradox.

.9... doesn't reach one.

It just represents the same value. We've been over this... Numbers aren't physical objects. They only exist in theory. What is the exact problem with .9... and 1 representing the same number?

You haven't explained this.

Originally Posted by A Roxxor

.9... doesn't reach one.

It just represents the same value.

That is the paradox. It never gets there, but it gets there. Get it?