Is 1 = 0.9999......

[silverpig]

Originally posted by: Kyteland
To those saying that 1/3 != 0.3333.... try doing the long division. They are the same.
...0.33333333333333...
3|1.00000000000000...
......9
......10
........9
........10
..........9
..........10
............9
............10
..............9
..............10
................9
................10
..................9
..................10
....................9
....................10
......................9
......................10
........................9
........................10
..........................9
..........................1

etc.

:beer:

And I'm gonna rip off your formatting for this:

...0.99999999999999...
1|1.00000000000000...
......9
......10
........9
........10
..........9
..........10
............9
............10
..............9
..............10
................9
................10
..................9
..................10
....................9
....................10
......................9
......................10
........................9
........................10
..........................9
..........................1

 

[MadRat]

Originally posted by: silverpig

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That would be true if you want to ignore a place value of .000...1.

 

[RossGr]

Originally posted by: MadRat

Originally posted by: silverpig

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That would be true if you want to ignore a place value of .000...1.

why do you ignore the fact that .000...1 + .999.... = 1+ .000...999... so is greater then 1. No matter where you put the 1 there are more 9s.

Just had a realization! I have allways thought Madrat = angry rodent, I was wrong

Madrat = Insane Rodent

 

[godspeedx]

I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

 

[DrPizza]

Originally posted by: godspeedx
I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

Not a proof, but *SHOULD* be a reasonable enough illustration of the fact that would convince most people. But then again, there are still people who believe the earth is flat, no matter what they're told... no matter what evidence is presented to them. Unfortunately, it's now appearing that a subset of those people are posting in this thread on ATOT.

 

[GoodToGo]

Originally posted by: silverpig

Originally posted by: Kyteland
To those saying that 1/3 != 0.3333.... try doing the long division. They are the same.
...0.33333333333333...
3|1.00000000000000...
......9
......10
........9
........10
..........9
..........10
............9
............10
..............9
..............10
................9
................10
..................9
..................10
....................9
....................10
......................9
......................10
........................9
........................10
..........................9
..........................1

etc.

:beer:

And I'm gonna rip off your formatting for this:

...0.99999999999999...
1|1.00000000000000...
......9
......10
........9
........10
..........9
..........10
............9
............10
..............9
..............10
................9
................10
..................9
..................10
....................9
....................10
......................9
......................10
........................9
........................10
..........................9
..........................1

Wow, just wow. How on earth did you come to this division? This result above is giving me a migraine.

Basically:
If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That has to be the worst proof ever. How do you define big and small?

 

[RossGr]

That has to be the worst proof ever. How do you define big and small?

While you might not like it that is the core to the fundamental proof.

the link in my sig contains 2 proofs, one relies on the convergence of the geometric series, the 2nd is a formal presentation of the above idea. Take a look at it, Ponder it, attempt to understand it. Then come back and ask questions.

 

[MAME]

Originally posted by: MadRat

Originally posted by: MAME
.999...9998 is not a real number, you can't have an infinite amount of 9's and then at an 8 to it. It's pointless arguing about this with people who refuse to look at the proof already provided by people who are much smarter than us

I find people that claim to be smarter than everyone else or depend on people telling them that they are smarter than everyone else to be retarded. So far there has been no proof to show that .999... exists. If .999... exists then it is plausible that .999...8 exists, so don't be so sure it a pointless argument.

I never said I was smarter than anyone. I implied people who have devoted their entire life to math are smarter. .999...998 does not exist. .999... does exists, here's how you get it:
1/3 = .333....
1/3 + 1/3 + 1/3 = .999.... Don't believe me? Do the math.

Now please give me some numbers I can add to get .999...998, I'm dying to know

 

[MAME]

Originally posted by: RossGr

Originally posted by: MadRat
Funny how we're to believe that .999... = 1 when no other infinite pattern of digits in a decimal would. We are to believe the digit nine is a magic number in this way.

I for one still believes an infinitely small remainder is the difference between 1 and .999... making 1 <> .999... as true. There has not been one solid proof to show otherwise.

9 is the magic digit in decimal
1 is the magic digit in binary (.111... = 1 (Binary)
2 is the magic digit in ternary (.222...=1 (Ternary)
3 is the magic digit in base 4 (.333...=1 Base 4)

need I continue?

The proof does not exist for you simply cuz you are incapable of comprehending it. Your preconceptions limit you.

Ross > Madrat

 

[MAME]

Originally posted by: DrPizza
No way, YamahaXS, I've read the entire thread (not all at once, but catch up every time I see it)...

Let me pose this question for bleeb and any others who think they're correct that .999... != 1
would you be willing to wager $100 on it? (I'm willing to bet that .999repeating EQUALS EXACTLY 1)

To settle the bet, 1st we each put our $100 someplace where the loser can't renig. Then, we put the names of all accredited universities that have a math program in a hat (or narrow the choices to just U.S. universities to eliminate the language barrier... I'm not sure I'd know how to ask profs at a chinese university). We then pull out 10 names at random and contact the math faculty of those universities. We'll go with whatever the majority of them agree upon (actually, I'd almost be willing to bet an additional $100 that it'll be unanimous that they say .999repeating = exactly 1.

Then again, that would be followed with someone starting a thread about how 10 out of 10 randomly selected college level math programs...



Let me offer not a proof, but perhaps a visual demonstration that some of you may be able to follow (can't remember if this one was shown yet or not)

2/7 = .285714285714285714285714285714285714285714285714285714...
5.7 = .714285714285714285714285714285714285714285714285714285...

Note: 2/7 + 5/7 equals exactly 1
Now, notice what happens if you were to add the two.
you get .99999999999999999999999999999999 repeating forever.

You are correct. What's funny to me is that while all these people who study math and are experts in the field, non of these .999... != 1 people won't listen to what they say. Yeah, I don't want a dentist working on my teeth either, I'd prefer a construction worker.

 

[Chu]

Originally posted by: MadRat

Originally posted by: silverpig

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That would be true if you want to ignore a place value of .000...1.

Some history here might be informative. I think you really need to think about the exact definition of "...". Something better then repeat forever. Before the field of real analysis came to be, math in general was plagued by problems relating to the nature of infinity, because everyone had a different definition of exactly what infinity was. These problems really came to a head when Fourier published a paper on the nature of infinite series of periodic functions. Because there wern't strict notions of how to treat functions as they approached infinitiy (this being 200 years after the calculus was discovered . . . the definition we use for limit today was still not in use) people had vastily different interpretations of fourier series, and the equivalent of this flame war began in mathematical circles over very similar problems.

-Chu

 

[MAME]

Originally posted by: Chu

Originally posted by: MadRat

Originally posted by: silverpig

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That would be true if you want to ignore a place value of .000...1.

Some history here might be informative. I think you really need to think about the exact definition of "...". Something better then repeat forever. Before the field of real analysis came to be, math in general was plagued by problems relating to the nature of infinity, because everyone had a different definition of exactly what infinity was. These problems really came to a head when Fourier published a paper on the nature of infinite series of periodic functions. Because there wern't strict notions of how to treat functions as they approached infinitiy (this being 200 years after the calculus was discovered . . . the definition we use for limit today was still not in use) people had vastily different interpretations of fourier series, and the equivalent of this flame war began in mathematical circles over very similar problems.

-Chu

Rock on.

If something goes forever, madrat, you can't add something to the end of it. You lose.

 

[GoodToGo]

Originally posted by: MAME

Originally posted by: Chu

Originally posted by: MadRat

Originally posted by: silverpig

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That would be true if you want to ignore a place value of .000...1.

Some history here might be informative. I think you really need to think about the exact definition of "...". Something better then repeat forever. Before the field of real analysis came to be, math in general was plagued by problems relating to the nature of infinity, because everyone had a different definition of exactly what infinity was. These problems really came to a head when Fourier published a paper on the nature of infinite series of periodic functions. Because there wern't strict notions of how to treat functions as they approached infinitiy (this being 200 years after the calculus was discovered . . . the definition we use for limit today was still not in use) people had vastily different interpretations of fourier series, and the equivalent of this flame war began in mathematical circles over very similar problems.

-Chu

Rock on.

If something goes forever, madrat, you can't add something to the end of it. You lose.

Finally sense prevails.

 

[MadRat]

If .999... has no end then it has no segments and therefore has no finite value therefore is not a real number. So it must not exist on a number line which means you're wrong saying .999...=1.

 

[MadRat]

Originally posted by: godspeedx
I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

1/3 = .333... with a remainder of 1/3 at the infinite position.
2/3 = .666... with a remainder of 2/3 at the infinite position.
3/3 = 1

 

[mchammer187]

Originally posted by: MadRat

Originally posted by: godspeedx
I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

1/3 = .333... with a remainder of 1/3 at the infinite position.
2/3 = .666... with a remainder of 2/3 at the infinite position.
3/3 = 1

a remainder cannot exist at the infinite position

how can you claim that .99.. does not exist thus is not a real number

but a number .00.................1 does

the 1 follows an infinite stream of zeros

well if there is a one after than it must terminate or else you cannot claim that the string of zero's is infinite

.99999999999999999999............... =1 it does exist
and .00000...........1 does not exist

 

[silverpig]

Originally posted by: MadRat
If .999... has no end then it has no segments and therefore has no finite value therefore is not a real number. So it must not exist on a number line which means you're wrong saying .999...=1.

Oh for fvck sakes...

1 is an infinitely repeating decimal. 1 = 1.000...

Actually 1 = ...0001.000...

So 1 has no segments and therefore has no finite value therefore is not a real number? So it must not exist on a number line?

 

[silverpig]

Originally posted by: GoodToGo

Originally posted by: silverpig
Basically:
If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That has to be the worst proof ever. How do you define big and small?

It's not a complete proof. I was outlining a proof very informally. It works though. Look at Ross's sig.

 

[RossGr]

Originally posted by: MadRat

Originally posted by: godspeedx
I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

1/3 = .333... with a remainder of 1/3 at the infinite position.
2/3 = .666... with a remainder of 2/3 at the infinite position.
3/3 = 1

There's that limited infinity again, so you see infintiy as point on the number line which can be reached?

Just not the case, until you can get a grasp on what we (ie Mathematicans) mean by infinity you ought stick to counting sheep. 1,2,3 Many.

 

[RossGr]

Originally posted by: MadRat
If .999... has no end then it has no segments and therefore has no finite value therefore is not a real number. So it must not exist on a number line which means you're wrong saying .999...=1.

So by your definition we must have .999... > 1

Why can I show that .999.... exists in the same intersection of intervals which can contain only the number 1.

Of course this is higher mathematics and you close your eyes to its existance.

 

[MadRat]

I don't claim .000...1 exists unless .999... exists. If .999... does not exist then .000...1 does not exist, too. Its a pretty simple deduction from philosophy. Either way, .999... does not equal one. I've shown why over and over. Simply saying that we cannot use conventional logic to relate .999... to 1 is the rawest truth, being that one is finite and the other is infinite. On the other hand there are people here that want to say that the truth actually reverses polarity when one throws infinity into the equation, but thats pure poppycock. The math whizzes around here seem to think that their flaws in philosophy are okay because it solves their absurd comparison. I think not.

 

[MadRat]

Originally posted by: RossGr

Originally posted by: MadRat
If .999... has no end then it has no segments and therefore has no finite value therefore is not a real number. So it must not exist on a number line which means you're wrong saying .999...=1.

So by your definition we must have .999... > 1

Why can I show that .999.... exists in the same intersection of intervals which can contain only the number 1.

Of course this is higher mathematics and you close your eyes to its existance.

By my definition, if we agree that .999... exists then .999... < 1 --- that is, remember, if we agree it exists at all.
If we agree it does not exist then by my definition the answer is simply that .999... <> 1.

Do you agree or disagree it exists on the real number line?

 

[MadRat]

Originally posted by: silverpig

Originally posted by: GoodToGo

Originally posted by: silverpig
Basically:
If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

That has to be the worst proof ever. How do you define big and small?

It's not a complete proof. I was outlining a proof very informally. It works though. Look at Ross's sig.

It does not work. The reference to .000...1 refers to the remainder at the infinite position when one subtracts .999... from 1. Adding .000...1 to .999... simply sums to 1. So in effect, the difference between 1 and .999... works perfectly fine if we agree that .999... exists at all on the number line. Any number on the number line should be able to be halved. If you try to halve .999... then you do not get .5, but rather we find the last of the nines cannot be divided so no division can really be done at all. If you halve something then the decimal should end in either a 5 or 0. If you try to half a nine then you get 4.5 which doesn't make for a very precise slit when we're talking an infinite number of nines to split. So basically if we could divide .999... in half then we'd get .4999...5, which you would suggest is not possible. (The ... in this case represent all 9's, not .499949994999....) If we divide 1 in half then we get .5, which clearly is not .4999...5.

 

[mchammer187]

Originally posted by: MadRat
I don't claim .000...1 exists unless .999... exists. If .999... does not exist then .000...1 does not exist, too. Its a pretty simple deduction from philosophy. Either way, .999... does not equal one. I've shown why over and over. Simply saying that we cannot use conventional logic to relate .999... to 1 is the rawest truth, being that one is finite and the other is infinite. On the other hand there are people here that want to say that the truth actually reverses polarity when one throws infinity into the equation, but thats pure poppycock. The math whizzes around here seem to think that their flaws in philosophy are okay because it solves their absurd comparison. I think not.

you claim that .00......1 doe not exist unless .999.........exists

i claim .999.. exists

.00000..1 can not exist by the definition of infintiy unless it has a value of zero

and .999999 ........ on the number line is "1"

it does not converge to one it does not approach one it IS 1
1 - .999 = .00..............1 anything that follows an infinite string of zeros is zeros


i dont understand how .9999......... is infinite

just because it has an infinite number of digits does not mean it does not exist

are you telling me Pi is not a real number so the ratio between the area of a circle to the radius does not exist because it has an infinite number of digits

 

[MadRat]

Originally posted by: mchammer187
are you telling me Pi is not a real number so the ratio between the area of a circle to the radius does not exist because it has an infinite number of digits

Pi does not have a fixed value, correct, so it does not exist on any exact place on a number line. We can approximate the location of Pi on a numberline, but we cannot find its exact value. As supercomputers become more powerful then the accepted value of Pi is extended further.