## 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...
9
33%
No, 1 ≠ 0.999...
14
52%
Other
4
15%

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

Magnus Anderson wrote:How do you observe endlessness?
How do you observe an absence of an end?
How do you observe absence in general?
Finally, what is an end?

I don't need to observe the far side of the Moon to know that it is there. As I said, Logic dictates.

phyllo wrote:There is no endless process.

There are no tireless minions endlessly calculating one digit after another.

Both processes and algorithms require sequential steps and therefore time to complete. Since there is no time involved, it's impossible for there to be any sort of process or algorithm.

Neither he nor I was talking about taking time. We were briefly discussing the implied process of converting a ratio into a decimal as a "process". He merely mentioned that it should be seen as a "completed process" and I mentioned that it is an "ENDLESS process", thus never "completed" regardless of any time requirements.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

I don't need to observe the far side of the Moon to know that it is there. As I said, Logic dictates.

Prediction refers to something that has been observed in the past that is expected to repeat in the future.

Everything has to be grounded in the observed. Otherwise, it is meaningless.

And such is the case with the concept of infinite. It is strictly speaking meaningless.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

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

Neither he nor I was talking about taking time. We were briefly discussing the implied process of converting a ratio into a decimal as a "process". He merely mentioned that it should be seen as a "completed process" and I mentioned that it is an "ENDLESS process", thus never "completed" regardless of any time requirements.
IOW, you redefined what the word 'process' means so that it suits your argument.

Okey-dokey.
phyllo
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### Re: Is 1 = 0.999... ? Really?

Magnus Anderson wrote:
I don't need to observe the far side of the Moon to know that it is there. As I said, Logic dictates.

Prediction refers to something that has been observed in the past that is expected to repeat in the future.

Not necessarily, but even so, an infinite series is a prediction from prior observation.

Magnus Anderson wrote:Everything has to be grounded in the observed. Otherwise, it is meaningless.

Actually everything has to be grounded in Logic, else literally meaningless. Meaning stems from subtle unconscious logic. One cannot even observe until certain aspects of logic are already operational.

Magnus Anderson wrote:And such is the case with the concept of infinite. It is strictly speaking meaningless.

Not to those who understand how reasoning works. When you observe that you can always add another number to whatever number you have, you can "predict" that there is no greatest number = "infinite".
phyllo wrote:
Neither he nor I was talking about taking time. We were briefly discussing the implied process of converting a ratio into a decimal as a "process". He merely mentioned that it should be seen as a "completed process" and I mentioned that it is an "ENDLESS process", thus never "completed" regardless of any time requirements.
IOW, you redefined what the word 'process' means so that it suits your argument.

Okey-dokey.

No one redefined, nor defined anything. Come up with a valid argument or follow Carleas.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

Not necessarily

Absolutely necessary. Any prediction that does not refer to something that has been observed in the past is meaningless.

Actually everything has to be grounded in Logic, else literally meaningless. Meaning stems from subtle unconscious logic. One cannot even observe until certain aspects of logic are already operational.

That's very backwards. Logic precedes sensations? Really?

Not to those who understand how reasoning works. When you observe that you can always add another number to whatever number you have, you can "predict" that there is no greatest number = "infinite".

That makes sense. But only because you think it does.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

Magnus Anderson
Philosopher

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Joined: Mon Mar 17, 2014 7:26 pm

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

No one redefined, nor defined anything. Come up with a valid argument or follow Carleas.
Carleas left because he got sick and tired of your nonsense.

Yeah, I think it's time to leave.
phyllo
ILP Legend

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

I am afraid this paradoxical forum harangues with the adage 'You can check in, but you can't check out, mate.
Meno_
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### Re: Is 1 = 0.999... ? Really?

You can only put up with someone saying "black is white" for so long. And this isn't the only thread where it has happened.
phyllo
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### Re: Is 1 = 0.999... ? Really?

phyllo wrote:
No one redefined, nor defined anything. Come up with a valid argument or follow Carleas.
Carleas left because he got sick and tired of your nonsense.

Yeah, I think it's time to leave.

Bullshit. He couldn't respond to my last question:
James S Saint wrote:
Carleas wrote:
James S Saint wrote:What is the limit as x goes to infinity for:
A) x?
B) 2x?
C) 2x+1?

The limits are all infinity.

So as x goes to infinity in your math$$_C$$, x converges with both 2x and also 2x+1. An interesting trick. Can you show us the convergence function for that?

And that means that all 3 have the range of x, the natural numbers. So after pairing to all of N, the set A is left out, unpaired, or alternatively, the second half of both sets N and A are left unpaired as well as "a".

Any time I ask a stumping question of Carleas, he either ignores it or simply disappears. He can never admit defeat (as most on this forum).

You guys continually make up distracting excuses, "you are redefining", "you are ignoring", "you are..." when the real truth is that your arguments are simply flawed. Whereas I need no excuses because what I state is coherent and logically valid.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

phyllo wrote:Carleas left because he got sick and tired of your nonsense.

Specifically, I lost interest after this post, in which James claimed that we can "only speculate" that $$P$$ is the domain of a function $$f:\, P \to N$$.

Between that and refusing to acknowledge the distinction between a set that is a subset of a set, and a set that is an element of a set, I got the impression that continuing the conversation would mean explaining why tautologies are true to someone who wouldn't admit it even if I could convince him.

Nah, I'm good.
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Carleas
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### Re: Is 1 = 0.999... ? Really?

Carleas wrote:
phyllo wrote:Carleas left because he got sick and tired of your nonsense.

Specifically, I lost interest after this post, in which James claimed that we can "only speculate" that $$P$$ is the domain of a function $$f:\, P \to N$$.

Between that and refusing to acknowledge the distinction between a set that is a subset of a set, and a set that is an element of a set, I got the impression that continuing the conversation would mean explaining why tautologies are true to someone who wouldn't admit it even if I could convince him.

Nah, I'm good.

Quite the opposite.

You try to inject irrelevant arguments to distract from the points being addressed. You quibble over what this or that word might mean to a mathematician versus common usage when those words hardly dictate anything relevant anyway. Meanwhile, you ignore the relevant arguments.

And it is certainly your speculation that your function covers the P domain. That is the whole crux of the argument. Oh but you just can't tolerate it being questioned. Geeezzz..

..just more excuses to divert from the fact that your bijection function has a serious problem that I finally managed to sufficiently expose. You haven't provided a valid bijection function and you can't because N cannot pair with N plus A.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

To be perfectly honest with everyone in this thread, nobody on earth actually knows why some rational numbers numbers do or don't terminate such that this question even arises. Doesn't happen with multiplication. This whole thread and all of these proofs are nonsense until someone solves that.
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:To be perfectly honest with everyone in this thread, nobody on earth actually knows why some rational numbers numbers do or don't terminate such that this question even arises.

Nonsense!

Take 10/3 = 3.333... <-- We know that 10 divided by 3 gives us 3 and a little bit. No mystery there. What is that little bit? It's 1/3. Dividing 1 by 3 is the same as dividing 10 by 3 except an order of magnitude lower. So we should get similar results: 1/3 = 0.3 and a little bit? How much is that little bit? It's 0.1... and it continues. <-- There's no mystery to this. We know why we get 3.333... when we divide 10 by 3. It's just a pattern that reinforces itself on every magnitude lower.
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gib
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### Re: Is 1 = 0.999... ? Really?

gib wrote:
Ecmandu wrote:To be perfectly honest with everyone in this thread, nobody on earth actually knows why some rational numbers numbers do or don't terminate such that this question even arises.

Nonsense!

Take 10/3 = 3.333... <-- We know that 10 divided by 3 gives us 3 and a little bit. No mystery there. What is that little bit? It's 1/3. Dividing 1 by 3 is the same as dividing 10 by 3 except an order of magnitude lower. So we should get similar results: 1/3 = 0.3 and a little bit? How much is that little bit? It's 0.1... and it continues. <-- There's no mystery to this. We know why we get 3.333... when we divide 10 by 3. It's just a pattern that reinforces itself on every magnitude lower.

You're misunderstanding.

When you multiply whole numbers, you never get a number like: 64.786...

When you divide numbers, sometimes the answer is something like: 0.5 or 1.3...

0.5 terminates, 1.3... terminates into infinite regress (keeping it rational)

There's an even finer point to this mystery that is often overlooked. When you place a bar over the 3 to signify its rational repetition, the threes actually regress, technically, at no point are those 3's actually repeating!!

You seem to think that just because you have learned how to divide into decimals that you actually understand why some numbers terminate and others infinitely regress. I assure you, you have no clue.
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

You can multiply any two natural numbers but you cannot divide any two natural numbers.

Operations have limits. They cannot operate on any kind of input you feed into them.

You cannot, for example, take $$3$$ apples and divide them in $$5$$ sets of equal number of apples. $$\frac{3}{5}$$ is an impossible operation. But you can say that this impossible operation is equal to some other impossible operation such as $$\frac{6}{10}$$.

When we say $$\frac{3}{5}=0.6$$ that's all we're saying: that $$\frac{3}{5}=\frac{6}{10}$$.

Decimal number is simply a fraction of the form $$\frac{a}{10^n}$$.

$$\frac{1}{3}$$ gives you a non-terminating decimal when you try to represent it in decimal form because there is no natural number that you can multiply by $$3$$ and get some power of ten.

There is absolutely nothing mysterious here.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

Magnus Anderson
Philosopher

Posts: 3712
Joined: Mon Mar 17, 2014 7:26 pm

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

gib wrote:Take 10/3 = 3.333... <-- We know that 10 divided by 3 gives us 3 and a little bit. No mystery there. What is that little bit? It's 1/3. Dividing 1 by 3 is the same as dividing 10 by 3 except an order of magnitude lower. So we should get similar results: 1/3 = 0.3 and a little bit? How much is that little bit? It's 0.1... and it continues. <-- There's no mystery to this. We know why we get 3.333... when we divide 10 by 3. It's just a pattern that reinforces itself on every magnitude lower.

.. and that is why it can never, ever resolve to be equal to it's fraction .. that "..and a little bit" never, ever goes away.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

Magnus Anderson wrote:You can multiply any two natural numbers but you cannot divide any two natural numbers.

Operations have limits. They cannot operate on any kind of input you feed into them.

You cannot, for example, take $$3$$ apples and divide them in $$5$$ sets of equal number of apples. $$\frac{3}{5}$$ is an impossible operation. But you can say that this impossible operation is equal to some other impossible operation such as $$\frac{6}{10}$$.

When we say $$\frac{3}{5}=0.6$$ that's all we're saying: that $$\frac{3}{5}=\frac{6}{10}$$.

Decimal number is simply a fraction of the form $$\frac{a}{10^n}$$.

$$\frac{1}{3}$$ gives you a non-terminating decimal when you try to represent it in decimal form because there is no natural number that you can multiply by $$3$$ and get some power of ten.

There is absolutely nothing mysterious here.

You're regurgitating, but not understanding. All of us know that stuff.

All of us know 3 doesn't divide into 10 without infinite regress using those techniques - nobody knows WHY!!

Why is it that every even and odd whole number terminates with even numbers, but not necessarily odd ones??

WHY??

I know you can parrot shit.

The whole point, is that we might actually be doing division wrong!
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Yes, you are right, we are doing division wrong. That must be it. It's not because division simply does not operate on certain values. No, it's that we're doing division wrong because every operation must operate on any kind of value we feed it into it. Nothing should have limits, everything should be without limits, so that when morons such as Ecmandu come along and do whatever they want to do they can never be accused of doing things the wrong way.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

Magnus Anderson
Philosopher

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

Magnus, WHY do some ODD numbers cause infinite regress?

WHY?!!

The proofs one way or another are meaningless until you answer that question.

Until then, you're just like someone who says small government exists because people say it does.

You either have a federal electorate or a non- federal non- elected corporatocracy, which in BOTH instances is big government.

You're a parrot, not a critical thinker
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:You're a parrot, not a critical thinker

No, he isn't.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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

James S Saint wrote:
Ecmandu wrote:You're a parrot, not a critical thinker

No, he isn't.

That's not an argument. Prove it.

I proved that occasionally some odd numbers cause infinite regress in this system, evens never do.

It's obvious that until someone figures out why these exceptions occur in this system, not just that they do, that these proofs one way or the other are incoherent.
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Ecmandu wrote:Magnus, WHY do some ODD numbers cause infinite regress?

WHY?!!

You need to explain to me how some odd numbers cause infinite regress. I have no idea what you're talking about, in other words.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

Magnus Anderson
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Joined: Mon Mar 17, 2014 7:26 pm

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

Ecmandu wrote:Magnus, WHY do some ODD numbers cause infinite regress?

It's an artifact of the decimal number system. $$\frac{1}{3}$$ is .333... in the decimal system, but it's .1 in base 3.

I'd guess (but haven't confirmed) that even numbers cause infinite decimal expansions in odd-base number systems.

EDIT: $$\frac{1}{2}$$ in base 10 is .111... in base 3.
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Carleas
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### Re: Is 1 = 0.999... ? Really?

Carleas wrote:
Ecmandu wrote:Magnus, WHY do some ODD numbers cause infinite regress?

It's an artifact of the decimal number system. $$\frac{1}{3}$$ is .333... in the decimal system, but it's .1 in base 3.

I'd guess (but haven't confirmed) that even numbers cause infinite decimal expansions in odd-base number systems.

EDIT: $$\frac{1}{2}$$ in base 10 is .111... in base 3.

You could then argue that the divisor of base and its multipliers are "even"
Ecmandu
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### Re: Is 1 = 0.999... ? Really?

Carleas wrote:... in base 10 is .111... in base 3.
Yeah .. just a matter of recycling on the evens or recycling on the odds.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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