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...
10
33%
No, 1 ≠ 0.999...
15
50%
Other
5
17%
 
Total votes : 30

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

Postby phyllo » Tue Jul 05, 2016 1:21 pm

Is_Yde_opN wrote:0.99999... + infinitesimal = 1

Infinitesimal, which according to James, is not a number.
But then 0.999999.... is also not a number, I guess.
Like 1/3 =0.33333... is also not a number.
1/2 = 0.5 is a number.

Following this reasoning I think it's safe to say that in reality we can divide something in half but we can't divide it into three thirds, while we could again make four quarters of something.

I think I've cracked the code of this thread - If something can be perfectly known then it's real. If something can't be perfectly known as a thing or things then it's not real.
Discrete things.

0.9999.. is not a number.
infinitesimal.. is not a number.
Together they form a whole, a knowable one thing.
Now they are real.

Something like that.
Well, James says that you got it right.

Maybe you could explain PI , because I find it confusing.

And now that I can't write 1/9 = 0.111... , what should I be writing? And how do I do long division?
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Re: Is 1 = 0.999... ? Really?

Postby Is_Yde_opN » Tue Jul 05, 2016 2:04 pm

phyllo wrote:
Is_Yde_opN wrote:0.99999... + infinitesimal = 1

Infinitesimal, which according to James, is not a number.
But then 0.999999.... is also not a number, I guess.
Like 1/3 =0.33333... is also not a number.
1/2 = 0.5 is a number.

Following this reasoning I think it's safe to say that in reality we can divide something in half but we can't divide it into three thirds, while we could again make four quarters of something.

I think I've cracked the code of this thread - If something can be perfectly known then it's real. If something can't be perfectly known as a thing or things then it's not real.
Discrete things.

0.9999.. is not a number.
infinitesimal.. is not a number.
Together they form a whole, a knowable one thing.
Now they are real.

Something like that.
Well, James says that you got it right.

Maybe you could explain PI , because I find it confusing.

And now that I can't write 1/9 = 0.111... , what should I be writing? And how do I do long division?


Now without sarcasm, I think that 0.3333... = 1/3 but if we want to be really accurate then it's better to not use 0.3333... in any equation and instead keep the 1/3. Even to write the result of an equation as for example something like (1/3)*sqrt(2).
In that sense, pi would be a shorthand for writing 4*SUM[n,0->infinite]((-1)^n/(2n+1))

But here's the thing: 1/3 is not only a Rational number, it's also part of the Reals, so 0.33333.... is just a different kind of notation, a notation which at best is recognised as a different notation for the accurate 1/3 notation, at worst is used like an approximation.

As for 0.999999.... being 1. I think it is the equal number for someone who recognises it as a different notation for 1, a notation which kind of implies 1.0.
At worst it's taken as an approximation which is never accurate. That is, if one takes the decimal places as literally the number and then finds that there is always one missing.
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Tue Jul 05, 2016 2:47 pm

Pi is a specific ratio that cannot be written in decimal form. There are a great many known relationships that cannot be represented in decimal form. And any and every decimal number that requires a ellipsis is not the actual limit for the same reason the decimal representations of Pi (even out to the 12 trillion places) is not the actual number. Infinite means that the string keeps going AND NEVER GETS TO THE NUMBER.
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".
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Re: Is 1 = 0.999... ? Really?

Postby Carleas » Tue Jul 05, 2016 4:06 pm

James S Saint wrote:You do NOT know its length. You only know it to be infinite.

These two sentences are mutual incompatible. We know its length to be infinite. That is a known length.

James S Saint wrote:
Carleas wrote:Two infinite sets are the same size if there's a function that uniquely maps every member of one set onto a member of the other set (i.e., it's a bijection).

Well that is true. The problem is that you can't actually do that.

I showed two examples, specifically addressing your claims that 1+infinity > infinity, and that two line segments of different lengths have different numbers of points. If you think my reasoning is flawed, show your work.

James S Saint wrote:Infinite means that there is no "there"... There is no "at infinity" to be finally reached...Why do you think that you can represent the solution that would be obtained "at infinity" when there is no "at infinity"?

You seem to be using a notion of infinity as somehow uncertain. But infinite quantities are certain, they are static, they're just infinite. They aren't growing or changing, we aren't waiting for them to get somewhere, they are just infinite. An infinite string isn't a process. An infinite string of 3s isn't growing, we aren't actually doing long division when refer to it. 1 divided by 3 produces an infinite, repeating decimal expansion .333... That infinite expansion is how 1 divided by 3 is written.

We can show that .333... equals 1/3, using a point you made earlier:

.333... = 3/10 + 3/100 +3/1000 ...

Multiply each side by 10:

10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 ...

Subtract the first equation from the second:

9(.333...) = 3
.333... = 3/9 = 1/3


[EDIT: left off a zero in one of the equations]
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Re: Is 1 = 0.999... ? Really?

Postby iambiguous » Tue Jul 05, 2016 7:17 pm

James,

I wonder how this guy would weigh in here: viewtopic.php?f=4&t=178452&hilit=kenneth

That's what this thread reminds me of.

70 pages later and still nothing actually resolved.

How long will this one go?

And one might surely assume that the truth here would transcend dasein!

Ah, the mystery of "reality" itself!

You know, objectively. :wink:
Objectivists: Like shooting fish in a barrel!

He was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles

Start here: viewtopic.php?f=1&t=176529
Then here: viewtopic.php?f=15&t=185296
And here: viewtopic.php?f=1&t=194382
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Re: Is 1 = 0.999... ? Really?

Postby phyllo » Tue Jul 05, 2016 7:24 pm

James S Saint wrote:Pi is a specific ratio that cannot be written in decimal form. There are a great many known relationships that cannot be represented in decimal form. And any and every decimal number that requires a ellipsis is not the actual limit for the same reason the decimal representations of Pi (even out to the 12 trillion places) is not the actual number. Infinite means that the string keeps going AND NEVER GETS TO THE NUMBER.
IOW, the symbol PI is just like the symbol 0.999... - both represent numbers which cannot be written out exactly in decimal form.

Yet you obsess about the 0.999... symbol.
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Tue Jul 05, 2016 7:52 pm

Carleas wrote:
James S Saint wrote:You do NOT know its length. You only know it to be infinite.

These two sentences are mutual incompatible. We know its length to be infinite. That is a known length.

Infinite is NOT a length. It is a quality. You already agreed that not all infinites are equal.

Carleas wrote:
James S Saint wrote:
Carleas wrote:Two infinite sets are the same size if there's a function that uniquely maps every member of one set onto a member of the other set (i.e., it's a bijection).

Well that is true. The problem is that you can't actually do that.

I showed two examples, specifically addressing your claims that 1+infinity > infinity, and that two line segments of different lengths have different numbers of points. If you think my reasoning is flawed, show your work.

A little off topic, so just briefly:
You can specify a particular infinite list, say the integers. And you can specify that you are going to take every other number, which you call "even" to make another list. In so doing, you have already stated that you only took half of the first list to make the second list. QED.

Alternatively you can specify the first list as the integers. And then specify a second list as 2 times each of the first list. In such a case, you have two equal cardinality lists. The problem is that you cannot multiply 2 times the maximum/last element of the first list, because there isn't such a maximum/last (NOT, NOT, NOT because you didn't have time to get to it). Thus you can't actually fulfill your second list specification. QED.

In either case, you cannot actually accomplish what you imagined doing.

Carleas wrote:
James S Saint wrote:Infinite means that there is no "there"... There is no "at infinity" to be finally reached...Why do you think that you can represent the solution that would be obtained "at infinity" when there is no "at infinity"?

You seem to be using a notion of infinity as somehow uncertain.

Not at all. "Infinity" is certainly not existent.
Carleas wrote: But infinite quantities are certain, they are static, they're just infinite. They aren't growing or changing, we aren't waiting for them to get somewhere, they are just infinite.

Except that there are different infinites. And even if you did know the number of items in the infinite list, you still would not know their sum, only their limit. Different size infinite sets can have the same summation limit. The limit DOES NOT specify the final summation.

Carleas wrote: An infinite string isn't a process. An infinite string of 3s isn't growing, we aren't actually doing long division when refer to it. 1 divided by 3 produces an infinite, repeating decimal expansion .333... That infinite expansion is how 1 divided by 3 is written.

That is an issue with you, not me. As I have said many times, I am not referring to the process unless I state that I am. There are different cardinalities and/or sizes of infinite. Which one do you have? You don't know. What is the sum of all of its elements? You don't know that either. All you know is the digits involved and the limit which is being eternally approached without ever, ever, ever being reached. It is certain that the limit is NOT reached, which is why it is an infinite, never ending string, with an always present remaining difference to 1.0 not summed.

You keep thinking that by stating that it is infinite, you have specified the end point of the string, "infinity", and thus of the summation. There is no end point to specify. And the summation never tallies as anything because it never ends. Even if you have added an infinite quantity of elements, you still have an infinite quantity to go. And you always do. It is "statically" unknown as to how many elements there are. You only know that it is an endless list.

Carleas wrote:We can show that .333... equals 1/3, using a point you made earlier:

.333... = 3/10 + 3/100 +3/100 ...

Multiply each side by 10:

10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 ...

Subtract the first equation from the second:

9(.333...) = 3
.333... = 3/9 = 1/3

Fault. 9 times 0.333... is NOT 3.0.
What is 9 times 3? 27.
Carried infinitely gives you: 2.999....
You merely presumed the consequent.

And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...

You know that every element in the infinite list:
    0.1
    0.01
    0.001
    .
    .
    .
has a 1 at the end. And you know that such is the entire list of the differences between 1 and ALL partial sums of the 0.999... series. Yet you keep insisting that "the final sum" has zero difference. Where did the 1 disappear to in that "final sum"? It is required to be in the specified list.
    A) there is NO FINAL SUMMATION.
    B) Even if there was a final summation, there would still be required a difference between it and 1.0
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".
.
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Re: Is 1 = 0.999... ? Really?

Postby One Liner » Tue Jul 05, 2016 8:19 pm

A poor analogy would be to say that my dog is the same as a picture of my dog (even though we say "that's my dog" when we look at a picture of my dog).
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Re: Is 1 = 0.999... ? Really?

Postby Carleas » Tue Jul 05, 2016 8:37 pm

James S Saint wrote:9 times 0.333... is NOT 3.0.

It looks as though, rather than finding a fault in my reasoning, you've just found a conclusion that you don't like. That equation, 9(.333...) = 3, is the result of subtracting this equation:

.333... = 3/10 + 3/100 +3/100 ...

from this equation:

10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 ...

So it can't be that the equation is faulty on its own. Either one of the previous equations must be incorrect, or the operation I performed on them was performed incorrectly. Which was it?
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Re: Is 1 = 0.999... ? Really?

Postby phyllo » Tue Jul 05, 2016 8:50 pm

Fault. 9 times 0.333... is NOT 3.0.
What is 9 times 3? 27.
Carried infinitely gives you: 2.999....
You merely presumed the consequent.
He didn't multiply by nine. The only multiplication that took place was the first multiplication by 10 and he only completed the operation on the right hand side. At the end, he divided both sides by 9 to get 0.333... =3/9
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Tue Jul 05, 2016 9:18 pm

Carleas wrote:
James S Saint wrote:9 times 0.333... is NOT 3.0.

It looks as though, rather than finding a fault in my reasoning, you've just found a conclusion that you don't like.

Bullshit Carleas. That YOU over and over
and over
and over
and over.


Carleas wrote: That equation, 9(.333...) = 3, is the result of subtracting this equation:

.333... = 3/10 + 3/100 +3/100 ...

from this equation:

10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 ...

So it can't be that the equation is faulty on its own.

James S Saint wrote:Fault. 9 times 0.333... is NOT 3.0.
What is 9 times 3? 27.
Carried infinitely gives you: 2.999....
You merely presumed the consequent.

And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...

Thus FAULT!!!
Do I need to repeat it 10 times??
James S Saint wrote:And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...
James S Saint wrote:And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...
James S Saint wrote:And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...
James S Saint wrote:And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...
James S Saint wrote:And when you "subtract" the two series, you get:
2.7 + 0.27 + 0.027 + ...

Which of course is 2.999..., NOT 3.000

THAT is the FAULT in your "reasoning" (just as I stated).
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".
.
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Re: Is 1 = 0.999... ? Really?

Postby One Liner » Tue Jul 05, 2016 9:34 pm

Actually, you repeated yourself 10 =
(0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...)x0.9999... times to be exact!
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Re: Is 1 = 0.999... ? Really?

Postby Carleas » Tue Jul 05, 2016 9:56 pm

.333... = 3/10 + 3/100 + 3/1000 + ...
10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 + ... = 3 + (3/10 + 3/100 + 3/1000...)

Is that not true?
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Re: Is 1 = 0.999... ? Really?

Postby phyllo » Tue Jul 05, 2016 10:52 pm

10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 + ... = 3 + (3/10 + 3/100 + 3/1000...)


which can be written as:

3.333...= 3 + 3/10 + 3/100 + 3/1000 + ... = 3 + (3/10 + 3/100 + 3/1000...)

So the question is :
Is the fractional bit in 3.333... exactly the same as it is in 0.333... ? Or is it different? Shorter by one digit? :D
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Wed Jul 06, 2016 2:17 am

Carleas wrote:.333... = 3/10 + 3/100 + 3/1000 + ...

That is true.
Carleas wrote:10 (.333...) = 3 + 3/10 + 3/100 + 3/1000 + ... = 3 + (3/10 + 3/100 + 3/1000...)

That is deceptive, but not false. The standard means for representation is lacking, thus leading to a deception.

phyllo wrote:Is the fractional bit in 3.333... exactly the same as it is in 0.333... ? Or is it different? Shorter by one digit? :D

That is exactly the issue.

What you have is:
[10.000... :0R] * [0.333... :3R] = [3.333... :30R]

Those are all of the same cardinality/size. But realize that you have stated that you multiplied EVERY element of the first series by 10. And that means EVERY element, no matter how infinite the list is. To maintain the same cardinality, you cannot have any added elements. And that means that the list of partial multiples will display that EVERY element is 10 times larger. And that means at the end of EVERY member of the infinite partial multiples list, you must have a place saver "0" that came from the multiple of 10 (just like you do with ALL arithmetics).
    0.3 --> 3.0
    0.03 --> 0.30
    0.003 --> 0.030
    .
    .
    .
    [0.000... :3R] --> [0.000... :30R]
EVERY element must have a zero place holder at the right end, else you did not multiply every element by 10.
That should be pretty obvious.


And that was the FAULT in your reasoning and the shortcoming of the standard method of representing any infinite series of digits.
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".
.
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Re: Is 1 = 0.999... ? Really?

Postby Carleas » Wed Jul 06, 2016 3:38 pm

James S Saint wrote:What you have is:
[10.000... :0R] * [0.333... :3R] = [3.333... :30R]

This is using hyperreals, which it seems you must to make your case. So, fair enough, if we use non-standard mathematical systems, we get a different result.
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Wed Jul 06, 2016 4:03 pm

Carleas wrote:
James S Saint wrote:What you have is:
[10.000... :0R] * [0.333... :3R] = [3.333... :30R]

This is using hyperreals, which it seems you must to make your case. So, fair enough, if we use non-standard mathematical systems, we get a different result.

You had an infinite set and then multiplied it times 10. What did you expect?

And it doesn't have to be hyperreals.
You had an infinite set of numbers then increased each by a factor of 10. So you still have an the infinite set of numbers. They are merely a little larger. But being larger, you must list them that way and thus maintain that "30" as the last number in the series. And of course, if you do that, when you add them all back together, you will still have that 30 at the extreme of the infinite set.
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".
.
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Posts: 25976
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Re: Is 1 = 0.999... ? Really?

Postby Carleas » Wed Jul 06, 2016 4:26 pm

James S Saint wrote:And it doesn't have to be hyperreals.

This sentence does have to be the hyperreals:
James S Saint wrote:EVERY element must have a zero place holder at the right end

There is no 'right end of infinity' in the standard reals. c.f. the hotel paradox, showing that infinity plus one is just infinity.
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Re: Is 1 = 0.999... ? Really?

Postby James S Saint » Wed Jul 06, 2016 5:09 pm

Carleas wrote:
James S Saint wrote:And it doesn't have to be hyperreals.

This sentence does have to be the hyperreals:
James S Saint wrote:EVERY element must have a zero place holder at the right end

There is no 'right end of infinity' in the standard reals. c.f. the hotel paradox, showing that infinity plus one is just infinity.

If EVERY member of an infinite set has a "right end", then the most extreme member also has a "right end".

You had an infinite set. EVERY member of that set had to have a "0" as its right digit because you multiplied every member by 10.

You don't throw away place holders when you add them all back together.

And if you count only the right side of the decimal, you still have the same quantity of digits as you started with .. as long as you count that last "30" as two digits, else you have a lesser infinity than you started with (which would constitute another Fault).
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?

Postby Carleas » Wed Jul 06, 2016 6:49 pm

James wrote:the most extreme member [of an infinite series]

Fault.

James S Saint wrote:EVERY member of that set had to have a "0" as its right digit because you multiplied every member by 10.

There's no difference between 1.0 and 1.00. As I argued earlier, there's an implied infinite string of zeros at the end of every real number that terminates.
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Re: Is 1 = 0.999... ? Really?

Postby Uccisore » Wed Jul 06, 2016 7:48 pm

James S Saint wrote:The "..." notation, specifically means that there is no end to be obtained. That means that it never, ever gets up to being exactly 1.0.


If that were true then that would confirm that 1.0 = .999... since the difference between them is 0.000... with 'no end to be obtained'. In order for the two numbers to be different, you'd have to propose that there is a '1' somewhere out there at the end of all those zeros, and you just said that in fact there is not.
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Re: Is 1 = 0.999... ? Really?

Postby phyllo » Wed Jul 06, 2016 7:52 pm

If EVERY member of an infinite set has a "right end", then the most extreme member also has a "right end".
It's funny how sometimes you can't get to the 'end' of an infinite string of digits and at other times you can say what the last digit is.

I guess it just depends on what better suits James' argument at the moment. :D
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Re: Is 1 = 0.999... ? Really?

Postby phyllo » Wed Jul 06, 2016 7:55 pm

If the symbol 0.333... means 0.333.....333 and also 0.333......330 (and 0.333.......300, etc ) then you got a serious problem brother.
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Re: Is 1 = 0.999... ? Really?

Postby Meno_ » Wed Jul 06, 2016 9:27 pm

There are no lines where the slope =0.Therefore all lines are circular,based on the relative slope of two parallel lines. There are no perfectly parallel straight lines.

Therefore all lines are curved as they approach countless spatial progressions.

Therefore the two curved parallel lines form two similar spheres.

Their similarity is implicit in the law of identity.

Therefore the principle of identity is dependent on the concept of infinite extension. The circle/sphere becomes the ideal representation for the infinite extension of the identity of infinitesimal parts as they approach either 0 or infinity. Here 1=1 is a conceivable and necessay description of tying up the infinitessimal with the infinife. It is a function of the symbolic notation.
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Re: Is 1 = 0.999... ? Really?

Postby Ultimate Philosophy 1001 » Thu Jul 07, 2016 3:16 am

jerkey wrote:There are no lines where the slope =0.Therefore all lines are circular,based on the relative slope of two parallel lines. There are no perfectly parallel straight lines.

Therefore all lines are curved as they approach countless spatial progressions.

Therefore the two curved parallel lines form two similar spheres.

Their similarity is implicit in the law of identity.

Therefore the principle of identity is dependent on the concept of infinite extension. The circle/sphere becomes the ideal representation for the infinite extension of the identity of infinitesimal parts as they approach either 0 or infinity. Here 1=1 is a conceivable and necessay description of tying up the infinitessimal with the infinife. It is a function of the symbolic notation.


Utter nonsense.

When a line is placed in a damping field, when zoomed out in sufficient scale in regards to the resolution, it has a slope of zero (according to the bounds of the resolution.)

a line in "digital code' can have an absolute slope of zero, as code cannot be zoomed in any further than what it is without ceasing to be code, zero is zero.

An lets say we are not talking about code but space.
Again this utter bonk
A line in a damping field can have it's sine wave compressed within typical bounds, if the damping field is infinite the slope will never curve onto itself.
And with no damping field there is no guarantee the line will even curve into itself and form a sphere, it will probably form a spiral, and eventually, a randomly shaped blob..
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