## Is 1 = 0.999... ? Really?

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## Is it true that 1 = 0.999...? And Exactly Why or Why Not?

Yes, 1 = 0.999...
13
41%
No, 1 ≠ 0.999...
16
50%
Other
3
9%

### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:Not really.

Magnus wrote:You are misusing the word "imply".

The algorithms you speak of do not "imply" infinite sequences. Properly speaking, they produce them as their output.

This is getting absurd on your part Magnus !

So...

When I state:

0.999. The algorithm as a closed set 9/10+9/100+9/1000 IMPLIES 0.999! It IMPLIES the OUTPUT!!!!

When I state 0.999...

The three dots IMPLY !! A rational number and IMPLIES infinite regress!
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Yes and I'm saying you are misusing the word "imply".
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:Yes and I'm saying you are misusing the word "imply".

There’s no output production without the implication.

Without implication, what does

1+1 equal?

It equals 1+1. !!

Without the implication 1+1 could NEVER equal 2!!!

Never!
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Either way, the output of an algorithm is not the algorithm itself. This is the central issue. And as usual, you are avoiding central issues by focusing on peripheral ones.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:Either way, the output of an algorithm is not the algorithm itself. This is the central issue. And as usual, you are avoiding central issues by focusing on peripheral ones.

No shit! I’ve said that many times already. The algorithm implies the sequence but is not the sequence. This whole nonsense line you brought me through is the only thing periphery to actual points that I made:

The actual point is that all sequences are derived from algorithms, implied from the algorithm, and can only be in time. If infinite sequences are outside of time (not motion itself but rather able to ALL be seen at once) then it contradicts the basic definition of endless and there’s no point to call them infinite.

Thus: infinite sequences are always processes
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

The fact that something is an output of an algorithm does not mean that it is an algorithm itself.
(It can be but not necessarily.)

Some algorithms output infinite sequences. But that does not mean that infinite sequences are algorithms. It simply does not follow.
(And no, they are not algorithms.)

You might as well say that you are the sex that your parents had when they decided to make you. But we all know that you aren't. You are merely a product of that sex.

You do not go around telling people that the process of Ecmandu's father having sex with Ecmandu's mother "implies" Ecmandu and that Ecmandu is therefore precisely that process: the process of Ecmandu's father having sex with Ecmandu's mother.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:The fact that something is an output of an algorithm does not mean that it is an algorithm itself.
(It can be but not necessarily.)

Some algorithms output infinite sequences. But that does not mean that infinite sequences are algorithms. It simply does not follow.
(And no, they are not algorithms.)

You might as well say that you are the sex that your parents had when they decided to make you. But we all know that you aren't. You are merely a product of that sex.

You do not go around telling people that the process of Ecmandu's father having sex with Ecmandu's mother "implies" Ecmandu and that Ecmandu is therefore precisely that process: the process of Ecmandu's father having sex with Ecmandu's mother.

And here’s you lying about what I said in the post above and STILL being on the periphery of my general and specific point (not responding to it!)...

viewtopic.php?p=2768200#p2768200

There’s probably an algorithm for birth, intent or not, and, again, totally on the periphery.

Project much?
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:No shit! I’ve said that many times already. The algorithm implies the sequence but is not the sequence.

You should have EXPLICITLY denied that the output of an algorithm and the algorithm itself are one and the same thing.

You should have said:

"No, the output of an algorithm is NOT the algorithm itself."

But you didn't.

Alright, so that's not what you think. Still, the problem remains. The fact that something is an output of an algorithm does not mean that it is an algorithm itself. It simply does not logically follow. The fact that $$2$$ is the output of an algorithm that outputs the sum of two integers does not mean that $$2$$ is an algorithm. Do you agree?

The actual point is that all sequences are derived from algorithms, implied from the algorithm, and can only be in time. If infinite sequences are outside of time (not motion itself but rather able to ALL be seen at once) then it contradicts the basic definition of endless and there’s no point to call them infinite.

The mathematical concept of sequence exists outside of time. (As do most of the mathematical entities.)

When we say that a sequence is endless, which means without an end, what that means is that there is no element within it that has the highest index (the element is otherwise known as "the last element".)
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:(not responding to it!)...

viewtopic.php?p=2768200#p2768200

Maybe because I was posting mine while you were posting yours?
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

So let’s do the “2 reply” of yours really quick!

2 is not an algorithm... right?

Actually!!! 2 IMPLIES EVERY ALGORITHM THAT EQUALS 2!!!

This is transitive !!

When I look at 1+1 I think of 2, when I look at 2, I think of 1+1!

It’s not accurate to state that a sequence is not the algorithm.

Can ANY being hold infinity in their minds at once?

If they can, it’s not infinity; if they can’t then infinity is a process!!
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:Can ANY being hold infinity in their minds at once?

And what does that mean?

Can you be more specific?

What does it mean to say that someone is holding infinity in their mind?
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

By the way, you have yet to address this:

Magnus wrote:An infinite sequence is not an algorithm for two reasons:

1) because algorithms are FINITE sequences (whereas infinite sequences are INFINITE sequences)

2) because algorithms are sequences of SPECIFIC THINGS (namely, instructions on how to perform a certain task) (whereas infinite sequences can be sequences of pretty much anything e.g. animals)

(Of course, this isn't the only thing you have yet to address. The list is quite long but for now I am only asking you to focus on this one.)

You made it clear that you agree that algorithms are finite sequences (and not infinite sequences.) I am happy about that. Given that algorithms are finite sequences, how can you say that infinite sequences are algorithms? By saying that infinite sequences are algorithms, you are saying that infinite sequences are finite sequences. Contradiction #1.

The other problem is that algorithms are sequences of INSTRUCTIONS whereas infinite sequences can be sequences of pretty much anything. So how can you say that sequences that can be sequences of pretty much anything are sequences that can only be sequences of instructions? Contradiction #2.

I am waiting for your response, Godot.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:By the way, you have yet to address this:

Magnus wrote:An infinite sequence is not an algorithm for two reasons:

1) because algorithms are FINITE sequences (whereas infinite sequences are INFINITE sequences)

2) because algorithms are sequences of SPECIFIC THINGS (namely, instructions on how to perform a certain task) (whereas infinite sequences can be sequences of pretty much anything e.g. animals)

(Of course, this isn't the only thing you have yet to address. The list is quite long but for now I am only asking you to focus on this one.)

You made it clear that you agree that algorithms are finite sequences (and not infinite sequences.) I am happy about that. Given that algorithms are finite sequences, how can you say that infinite sequences are algorithms? By saying that infinite sequences are algorithms, you are saying that infinite sequences are finite sequences. Contradiction #1.

The other problem is that algorithms are sequences of INSTRUCTIONS whereas infinite sequences can be sequences of pretty much anything. So how can you say that sequences that can be sequences of pretty much anything are sequences that can only be sequences of instructions? Contradiction #2.

I am waiting for your response, Godot.

Magnus, honestly, I’m just shaking my head and thinking you’re retarded.

I barely want to bother with you anymore right now.

I’ll just offer some lazy “throw-away” sentences to you.

A finite algorithm CAN (not always) imply an infinite sequence. An infinite sequence can conversely imply a finite algorithm.

Infinite sequences cannot be finite sequences (convergence at limits never occur).

You’re not even bothering anymore to quote my arguments and respond to them.

You’re projecting big time here. I’ve addressed all your arguments ... you’ve stopped addressing mine for many pages now. You’re cherry picking shit. You’ve been doing it for a while now.

Every fucking time you gave me an actual argument (and not your filler) I addressed it. Every time I respond to your actual argument, you don’t address it, you address the filler. And then tell me that I haven’t responded to vast swaths of what you’ve put forth.

It’s actually insulting. You know, it fucking takes time and energy to post. You had my undivided attention, and you just keep shitting on it by ignoring it.

2 = 1+1
1+1 =2

How fucking simple is that? The algorithm implies the number, the number implies the algorithm. Not a peep from you!

I even said that that’s not my fucking point!!! You’re making it a point for no reason at fucking all!!

My actual point is that no possible being in existence can hold infinity in their mind, because infinity doesn’t fucking end. How fucking simple is that? Very fucking simple!

If no being can hold infinity in their mind, than infinity is not an object, but a fucking VERB!!!!

The number 1 is a fucking NOUN!!! It’s a person, place or thing. Get it?!?!

Infinity is NOT a fucking noun!!! It’s an ACTION that never ends. Infinity is motion of the cosmos itself!

It’s getting old Magnus.

How about another point I raised to you that you ignored!?!?

You state that you can add and subtract on a single infinite string. You only use subtraction because you already know that addition is absurd.

0.333...666...

Is a number. You’d be laughed out of this thread so fast for saying that!!!!

So you only focus on “removal”

0.333...

And

0.0(333)...

Like several fucking people have already told you, if the zero moves up one step or the threes all move back one step, with infinite sets, they’ll all be holding hands again because infinity never fucking ends! I mean, honestly! This is like kindergarten shit!

Infinite sets don’t act the same as finite sets!!!

In a finite set, if you move forward one or back one, someone is not holding hands anymore!

That’s a fucking PROOF that the two sets behave differently (finite and infinite)!

I think you have spatial IQ issues, honestly, I do
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:I’ll just offer some lazy “throw-away” sentences to you.

Nothing new.

Not a single one.

If that's what you call undivided attention . . .

My actual point is that no possible being in existence can hold infinity in their mind

I asked you what that means. You chose not to respond. Typical.

You only use subtraction because you already know that addition is absurd.

Anyways, you have yet to address this post:

If you don't know what I mean by that, ask me, and I'll explain it to you. Don't simply assume you know what that means.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus,

I got mad at you because you’re cherry picking.

How fucking hard is it to understand the word: implied???

Honestly! Is it that fucking hard?

1+1 = 2
2 = 1+1

In the second one the solution is determined (implies) by the algorithm!!! In the first one, the algorithm determines (implies) the solution!
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### Re: Is 1 = 0.999... ? Really?

$$1 + 1$$ is not an algorithm. It is a mathematical expression that has the same meaning as $$2$$. Thus, we say, $$1 + 1 = 2$$. This too is a mathematical expression. What it says is that the expression $$1 + 1$$ and the expression $$2$$ have one and the same meaning.

The following, on the other hand, is an algorithm:

1) Set $$a$$ to an integer of your choice.
2) Set $$b$$ to an integer of your choice.
3) Set $$c$$ to 0.
4) Add the value of $$a$$ to $$c$$.
5) Add the value of $$b$$ to $$c$$.
6) Stand up and loudly proclaim the value of $$c$$.

This algorithm takes two integers as an input, calculates their sum and outputs it.

The above algorithm and the expression $$1 + 1$$ represent two different things.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:$$1 + 1$$ is not an algorithm. It is a mathematical expression that has the same meaning as $$2$$. Thus, we say, $$1 + 1 = 2$$. This too is a mathematical expression. What it says is that the expression $$1 + 1$$ and the expression $$2$$ have one and the same meaning.

The following, on the other hand, is an algorithm:

1) Set $$a$$ to an integer of your choice.
2) Set $$b$$ to an integer of your choice.
3) Set $$c$$ to 0.
4) Add the value of $$a$$ to $$c$$.
5) Add the value of $$b$$ to $$c$$.
6) Stand up and loudly proclaim the value of $$c$$.

This algorithm takes two integers as an input, calculates their sum and outputs it.

The above algorithm and the expression $$1 + 1$$ represent two different things.

Magnus,

Anything that uses an operator is an algorithm. Whether finite or infinite.

Besides that:

You have unary code. Unary code uses either spaces (instead of zeroes) or enter buttons (instead of zeroes) or both (a form of trinary) (for the SAME symbol)

Unary is either ‘binary’ or ‘trinary’ at the same time.

What does this mean to this discussion?

I don’t know!

But more to your post ((which was totally (again) off topic))

Anytime an operator is used to represent something else, it’s an algorithm. Algorithm is always defined an an implication:

No algorithm?

1+1=1+1

With an algorithm?

1+1=2

Implication! It means there’s implication!

Again! This is you avoiding content.

THIS argument is you criticizing filler instead of the actual point of this post (which you again, ignored)!!

viewtopic.php?p=2768225#p2768225
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:Anything that uses an operator is an algorithm. Whether finite or infinite.

Disagree.

Remember what I said earlier?

An infinite sequence is not an algorithm for two reasons:

1) because algorithms are FINITE sequences (whereas infinite sequences are INFINITE sequences)

2) because algorithms are sequences of SPECIFIC THINGS (namely, instructions on how to perform a certain task) (whereas infinite sequences can be sequences of pretty much anything e.g. animals)

You made it clear that you agree that algorithms are finite sequences (and not infinite sequences.) I am happy about that. Given that algorithms are finite sequences, how can you say that infinite sequences are algorithms? By saying that infinite sequences are algorithms, you are saying that infinite sequences are finite sequences. Contradiction #1.

The other problem is that algorithms are sequences of INSTRUCTIONS whereas infinite sequences can be sequences of pretty much anything. So how can you say that sequences that can be sequences of pretty much anything are sequences that can only be sequences of instructions? Contradiction #2.

You have yet to respond to this.

In the above, I made a number of claims. These are:

1) Algorithms are finite sequences.

2) Infinite sequences are infinite sequences.

3) Algorithms can only be sequences of instructions.

4) Infinite sequences can be sequences of anything.

5) If #1 and #2 are true, it follows that infinite sequences aren't algorithms.

6) If #3 and #4 are true, it follows that infinite sequences aren't algorithms.

Question #1:
Do you UNDERSTAND these statements?

Question #2:
Do you AGREE with them?

Question #3:
If you disagree with any of them, why do you disagree?

Answering these questions is what it means to address what I said in the above quotes.

Did you do such a thing so far?

Not really.
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:
Ecmandu wrote:Anything that uses an operator is an algorithm. Whether finite or infinite.

Disagree.

Remember what I said earlier?

An infinite sequence is not an algorithm for two reasons:

1) because algorithms are FINITE sequences (whereas infinite sequences are INFINITE sequences)

2) because algorithms are sequences of SPECIFIC THINGS (namely, instructions on how to perform a certain task) (whereas infinite sequences can be sequences of pretty much anything e.g. animals)

You made it clear that you agree that algorithms are finite sequences (and not infinite sequences.) I am happy about that. Given that algorithms are finite sequences, how can you say that infinite sequences are algorithms? By saying that infinite sequences are algorithms, you are saying that infinite sequences are finite sequences. Contradiction #1.

The other problem is that algorithms are sequences of INSTRUCTIONS whereas infinite sequences can be sequences of pretty much anything. So how can you say that sequences that can be sequences of pretty much anything are sequences that can only be sequences of instructions? Contradiction #2.

You have yet to respond to this.

In the above, I made a number of claims. These are:

1) Algorithms are finite sequences.

2) Infinite sequences are infinite sequences.

3) Algorithms can only be sequences of instructions.

4) Infinite sequences can be sequences of anything.

5) If #1 and #2 are true, it follows that infinite sequences aren't algorithms.

6) If #3 and #4 are true, it follows that infinite sequences aren't algorithms.

Question #1:
Do you UNDERSTAND these statements?

Question #2:
Do you AGREE with them?

Question #3:
If you disagree with any of them, why do you disagree?

Answering these questions is what it means to address what I said in the above quotes.

Did you do such a thing so far?

Not really.

Alright fine. You put in a very clear way “some meat on those bones”

It’s fine if you and I have to repeat ourselves at times...

1.) “algorithms are finite sequences)

Me: this is tautologically true; if an algorithm is infinite, it never stops to yield an output!!!

2.) “infinite sequences are infinite sequences”

Me: true, but also definitely false.

1/9 = 0.111...

Your word “are” also means “equals” in my case above, a finite expression “is” (are) equals an infinite expression.

3.) “algorithms can only be sequences of instructions”

Me: algorithms are finite instructions that imply the sequence. (Not sequences of instructions (You had it backwards)) Some are finite, some are infinite.

4.) “infinite sequences can be sequences of anything”

Me: umm... this is obviously not true. You’re going to kick yourself here. Sequence:(1,2,3) end sequence! Obviously that’s not infinite. The difference between you and I in this discussion is that I KNOW WHAT YOU MEAN!! So I’m not going to hold it against you!!

Let me take this to a side discussion... I used to HATE song lyrics (they always contradict themselves) and then I realized “but I still know what they mean”. And I don’t hate them as much. You contradicted yourself big time here, but I still know what you MEAN!!

What you meant to say is that “any variable can be used as an infinite placeholder”... that’s what you MEANT! You often don’t afford me the same luxury! (Which is why I get so frustrated with you)

5 and 6 are Simply syllogisms that imply the first 4 are true
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:1) Algorithms are finite sequences

Me: this is tautologically true; if an algorithm is infinite, it never stops to yield an output!!!

An algorithm does not need to halt in order to produce an output.

Consider a computer program that consists of an infinite number of one and the same statement: PRINT "HELLO WORLD". Such a program will never stop running, and yet, it will write to your console as frequently as possible.

The reason why algorithms are finite sequences is not because an infinite sequence of instructions cannot produce an output (that's not true) but quite simply due the definition of the word "algorithm".

https://en.wikipedia.org/wiki/Algorithm

Wikipedia wrote:In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation.

That's quite simply what the word means.

2) Infinite sequences are infinite sequences

Me: true, but also definitely false.

How can a statement be both true and false? Isn't that a logical contradiction?

3) Algorithms can only be sequences of instructions

Me: algorithms are finite instructions that imply the sequence. (Not sequences of instructions (You had it backwards)) Some are finite, some are infinite.

I have no idea what it means to say that algorithms are finite instructions. In fact, I am not aware of the difference between finite and infinite instructions. Can you clarify?

Wikipedia disagrees with you, though. Algorithms are defined as finite sequences of instructions.

4) Infinite sequences can be sequences of anything

Me: umm... this is obviously not true.

So an infinite sequence cannot consist of certain kinds of things? What kinds of things?

What you meant to say is that “any variable can be used as an infinite placeholder”... that’s what you MEANT!

I have no idea what that means.

You often don’t afford me the same luxury! (Which is why I get so frustrated with you)

The reason you get frustrated is because you don't know how to interact with people (specifically, how to discuss ideas with them.)

5 and 6 are Simply syllogisms that imply the first 4 are true

They don't imply the first four are true. Rather, they state if some of the previous statements are true, it follows that infinite sequences aren't algorithms.
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:
Ecmandu wrote:1) Algorithms are finite sequences

Me: this is tautologically true; if an algorithm is infinite, it never stops to yield an output!!!

An algorithm does not need to halt in order to produce an output.

Consider a computer program that consists of an infinite number of one and the same statement: PRINT "HELLO WORLD". Such a program will never stop running, and yet, it will write to your console as frequently as possible.

The reason why algorithms are finite sequences is not because an infinite sequence of instructions cannot produce an output (that's not true) but quite simply due the definition of the word "algorithm".

https://en.wikipedia.org/wiki/Algorithm

Wikipedia wrote:In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation.

That's quite simply what the word means.

2) Infinite sequences are infinite sequences

Me: true, but also definitely false.

How can a statement be both true and false? Isn't that a logical contradiction?

3) Algorithms can only be sequences of instructions

Me: algorithms are finite instructions that imply the sequence. (Not sequences of instructions (You had it backwards)) Some are finite, some are infinite.

I have no idea what it means to say that algorithms are finite instructions. In fact, I am not aware of the difference between finite and infinite instructions. Can you clarify?

Wikipedia disagrees with you, though. Algorithms are defined as finite sequences of instructions.

4) Infinite sequences can be sequences of anything

Me: umm... this is obviously not true.

So an infinite sequence cannot consist of certain kinds of things? What kinds of things?

What you meant to say is that “any variable can be used as an infinite placeholder”... that’s what you MEANT!

I have no idea what that means.

You often don’t afford me the same luxury! (Which is why I get so frustrated with you)

The reason you get frustrated is because you don't know how to interact with people (specifically, how to discuss ideas with them.)

5 and 6 are Simply syllogisms that imply the first 4 are true

They don't imply the first four are true. Rather, they state if some of the previous statements are true, it follows that infinite sequences aren't algorithms.

I’ll only respond here to your last statement in these replies.

Magnus wrote: “infinite sequences are not algorithms”

Infinite sequences ALWAYS, always IMPLY an algorithm!

How many times do I have to say this before you stop misquoting my intent?
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### Re: Is 1 = 0.999... ? Really?

So you agree that algorithms are finite sequences and you also agree that infinite sequences are infinite sequences (but you also disagree, for some reason.)

If you agree with both of these statements then to say that an infinite sequence is an algorithm is to say that an infinite sequence is a finite sequence which is a logical contradiction.

How do you respond to this?
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:So you agree that algorithms are finite sequences and you also agree that infinite sequences are infinite sequences (but you also disagree, for some reason.)

If you agree with both of these statements then to say that an infinite sequence is an algorithm is to say that an infinite sequence is a finite sequence which is a logical contradiction.

How do you respond to this?

Magnus,

This discussion has VERY little bearing on my points 3 pages ago, and I actually delved into it in a very complex way...

Let’s just chalk all this up to a minor “derail”

Like I explained before...

1/9 (very finite)

Also equals

1/10+1/100+1/1000+1/10000 etc...

In this way, Every finite number equals an infinite number of infinite series, the shorthand of which ... is an algorithm (the series is implied from the command)

As far as the topic of the thread is concerned:

Does 0.999... = 1. In the same way that 0.111... =1/9?

No, it does not!
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:1/9 = 0.111...

Your word “are” also means “equals” in my case above, a finite expression “is” (are) equals an infinite expression.

The way I understand it, what you're saying is:

1) $$0.111\dotso$$ is an infinite sequence.
(Disagree.)

2) $$\frac{1}{9}$$ is a finite sequence.
(Disagree.)

3) $$0.111\dotso = \frac{1}{9}$$ is true.
(Disagree.)

4) If #1, #2 and #3 are true, it follows that there is at least one infinite sequence that is a finite sequence.
(I'm inclined to agree with this.)

The problem is that $$\frac{1}{9}$$ and $$0.111\dotso$$ are not sequences. They are numbers. (And it's also not true that $$0.111\dotso = \frac{1}{9}$$ but that's a peripheral issue.)
Magnus Anderson
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:This discussion has VERY little bearing on my points 3 pages ago, and I actually delved into it in a very complex way...

Let’s just chalk all this up to a minor “derail”

This proves my point that you are not interested in a genuine discussion. Each time you are forced to interact with other people (rather than preach to them) you get uncomfortable.
Magnus Anderson
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