Is 1 = 0.9999......

[Woodchuck2000]

As proofs go, it's badly phrased in my opinion...
As i stated earlier, I've seen a much better proof of the proposition, I was just playing devil's advocate because josphII was bullsh*tting...

 

[AznMaverick]

don't you just love debates like this?

 

[Yomicron]

Originally posted by: Woodchuck2000
Yomicron - note how the thing posted was missing the '-' from -n, making it incorrect.

As i stated earlier, I've seen a much better proof of the proposition, I was just playing devil's advocate because josphII was bullsh*tting...

ahhh...I didn't see the post where you said that

as for the'-',
the 10^-n was made into 1/10^n

 

[Yomicron]

Originally posted by: ElFenix
gah! people who know nothing of number theory trying to bend their minds around it is horrible! this is as bad as the "you're on a game show and you've shown 3 doors and behind 2 are nothing and behind the other is a million bucks" question

Lets Make a Deal!


a thread on that problem would be entertaining

 

[DoNotDisturb]

someone give me the solutions to the navier stokes equations on fluid compression, and i'll give you a million dollars.

 

[FrustratedUser]

Since 0.999999.... is always going to be less than 1 ---> Not equal

 

[SilentRunning]

If a decimal accuracy is defined then 0.9999...... = 1

If no decimal accuracy is defined then the two numbers will never be equal.

Old school math.

 

[Siva]

when someone counts .99999 an infinite amount of times and tells me that one is way up there, i'll believe them

 

[TuxDave]

Originally posted by: McPhreak

Originally posted by: TuxDave
That proof looks good to me. I believe 0.9999... = 1. For those who don't believe still, show me 1-0.999... doesn't equal 0.

And if you say it equals 0.000000.....001... there's an infinite number of zeros, so that '1' never really exists, so technically 1-0.999... = 0

Does that mean 0.99999.....98 = 0.999999999.....99?

Ahh.. but there's a freaky difference. I say numbers like 0.9999....98 doesn't exist because we define there to be an infinite number of nines... and here with 0.9999...98 we say, there's a last nine, but there isn't.. there's infinite!

 

[TuxDave]

There's something I learned that may be causing ppl discomfort. If people claim that 0.9999... != 1, then they should also be comfortable to say that the largest number smaller than 1 is 0.9999..... Now here's a question, is there such thing as a largest number smaller than 1?

 

[FrustratedUser]

Originally posted by: TuxDave

Originally posted by: McPhreak

Originally posted by: TuxDave
That proof looks good to me. I believe 0.9999... = 1. For those who don't believe still, show me 1-0.999... doesn't equal 0.

And if you say it equals 0.000000.....001... there's an infinite number of zeros, so that '1' never really exists, so technically 1-0.999... = 0

Does that mean 0.99999.....98 = 0.999999999.....99?

Ahh.. but there's a freaky difference. I say numbers like 0.9999....98 doesn't exist because we define there to be an infinite number of nines... and here with 0.9999...98 we say, there's a last nine, but there isn't.. there's infinite!

Well, that means 0.999999.... is infinitely smaller than 1.

 

[silverpig]

Holy fsck people.


0.999... DOESN'T APPROACH ANYTHING. IT'S NOT GETTING LARGER.

It just IS 1.

You are still thinking about writing a zero, then adding a decimal point, and then adding a nine, then another, then another...

If you do that, then no, what you write down will never equal 1 because it's a progression. We are NOT talking about that though. We are talking about an already infinite string of 9s. Not a string to which you add nines without end. There is a HUGE difference.

Do the freaking subtraction.


1.0000000000000000000000 -
0.9999999999999999999999
---------------------------------------
0.0000000000000000000000

as you can clearly see, their difference is a 0, followed by a decimal point, followed by an infinite string of 0s. Or, as most normal folk like to call it, just plain ol' 0.

You can also do it by long division. I don't think anyone here will disagree with me when I say that 1/1 = 1 right? What if I could prove via long division that 1/1 = 0.999...?

You must be able to accept one thing though. We can say that 3 goes into 6 twice with a remainder of 0, or we can say that 3 goes into 6 once with a remainder of 3, or 0 times with a remainder of 6. All statements are equivalent. Keeping that in mind:

_____________________________________
1)1.000000000000000000000000000000000... <--- supposed to be 1 into 1.000...

Now, we can do it the easy way and say 1 goes into 1 once, remainder 0 and be done with it, or we can do the following:

1 goes into 1 0 times, remainder 1. We are left with:

_0.___________________________________
1)1.000000000000000000000000000000000...
__0

Now, let's do the subtraction.

_0.___________________________________
1)1.000000000000000000000000000000000...
__0
__10

Okay. Now let's say that 1 goes into 10 9 times, remainder 1.


_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9

Subtract.

_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___1

Bring down the 0

_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___10

1 goes into 10 9 times, remainder 1.

0.99___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___10
____9

repeat ad infinitum


I think the point is pretty obvious here.

 

[DoNotDisturb]

Originally posted by: silverpig
Holy fsck people.


0.999... DOESN'T APPROACH ANYTHING. IT'S NOT GETTING LARGER.

It just IS 1.

You are still thinking about writing a zero, then adding a decimal point, and then adding a nine, then another, then another...

If you do that, then no, what you write down will never equal 1 because it's a progression. We are NOT talking about that though. We are talking about an already infinite string of 9s. Not a string to which you add nines without end. There is a HUGE difference.

Do the freaking subtraction.


1.0000000000000000000000 -
0.9999999999999999999999
---------------------------------------
0.0000000000000000000000

as you can clearly see, their difference is a 0, followed by a decimal point, followed by an infinite string of 0s. Or, as most normal folk like to call it, just plain ol' 0.

You can also do it by long division. I don't think anyone here will disagree with me when I say that 1/1 = 1 right? What if I could prove via long division that 1/1 = 0.999...?

You must be able to accept one thing though. We can say that 3 goes into 6 twice with a remainder of 0, or we can say that 3 goes into 6 once with a remainder of 3, or 0 times with a remainder of 6. All statements are equivalent. Keeping that in mind:

_____________________________________
1)1.000000000000000000000000000000000... <--- supposed to be 1 into 1.000...

Now, we can do it the easy way and say 1 goes into 1 once, remainder 0 and be done with it, or we can do the following:

1 goes into 1 0 times, remainder 1. We are left with:

_0.___________________________________
1)1.000000000000000000000000000000000...
__0

Now, let's do the subtraction.

_0.___________________________________
1)1.000000000000000000000000000000000...
__0
__10

Okay. Now let's say that 1 goes into 10 9 times, remainder 1.


_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9

Subtract.

_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___1

Bring down the 0

_0.9___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___10

1 goes into 10 9 times, remainder 1.

0.99___________________________________
1)1.000000000000000000000000000000000...
__0
__10
___9
___10
____9

repeat ad infinitum


I think the point is pretty obvious here.

explain to me an infinite string of 9s and where u add 9s without an end....

 

[DoNotDisturb]

correct me if i'm wrong, if you're adding 9s without end, then you are implying no set limit because it goes on forever, and what is the definition of something that has no boundaries or set limits? you tell me.

 

[silverpig]

Infinite string:

We write 0.999... to represent an already infinite string of nines. The nines are already there.

Adding nines without end:

You start with a zero, then add a decimal point, then a nine, then another nine... ad infinitum. There is a progression towards the infinite string, but this string will never be infinite as it's time dependent.

 

[DoNotDisturb]

ah, it depends on time... good point, thx for correcting me.

 

[silverpig]

Originally posted by: DoNotDisturb
ah, it depends on time... good point, thx for correcting me.

 

[Jzero]

How about if you have an infinite string of nines compared to an infinite string of nines that is doubly long as the first? They are actually equal?

A hotel with an infinite number of rooms, every single room is filled.
Suddenly an infinite number of busses carrying an infinite number of people shows up.
Think quick! Tell everyone in an odd-numbered room to pack their crap, double their room number and get in there.
Suddenly you have infinitely more available rooms. Send the new guests into the odd-numbered rooms.

Infinite is infinite. No matter how many nines are at the end of the string, there could always be infinitely more nines. Both strings must be equal to 1, yeh they contain different infinities.
Perhaps in some fields it can be considered equal to 1. In others, it will always be 1/nth short.

 

[ElFenix]

Originally posted by: Yomicron

Originally posted by: ElFenix
gah! people who know nothing of number theory trying to bend their minds around it is horrible! this is as bad as the "you're on a game show and you've shown 3 doors and behind 2 are nothing and behind the other is a million bucks" question

Lets Make a Deal!


a thread on that problem would be entertaining

we did a year or two back. it got really long.


1 is an assumption anyway. so if the defintion of .999999... is 1, well, how do you say it isn't since 1 is assumed?

 

[GoingUp]

nope

 

[Einz]

Dunno if this has been posted yet, but this is how I was taught to think about it:

1/3 = 0.3333....
1/3*3=0.3333...*3
3/3=0.9999...

3/3 = 1, 0.9999... = 1

 

[silverpig]

Originally posted by: Einz
Dunno if this has been posted yet, but this is how I was taught to think about it:

1/3 = 0.3333....
1/3*3=0.3333...*3
3/3=0.9999...

3/3 = 1, 0.9999... = 1

REPOST!




had to

 

[Torghn]

Everyone who voted No either doens't know much about Math or is just stupid. Either way it seems it's the bulk of the people voting.

 

[silverpig]

Originally posted by: Jzero
How about if you have an infinite string of nines compared to an infinite string of nines that is doubly long as the first? They are actually equal?

A hotel with an infinite number of rooms, every single room is filled.
Suddenly an infinite number of busses carrying an infinite number of people shows up.
Think quick! Tell everyone in an odd-numbered room to pack their crap, double their room number and get in there.
Suddenly you have infinitely more available rooms. Send the new guests into the odd-numbered rooms.

Infinite is infinite. No matter how many nines are at the end of the string, there could always be infinitely more nines. Both strings must be equal to 1, yeh they contain different infinities.
Perhaps in some fields it can be considered equal to 1. In others, it will always be 1/nth short.

We're dealing with a cardinality of 0 here. Aleph-null I do believe. Other infinities don't apply

 

[TuxDave]

Originally posted by: FrustratedUser

Originally posted by: TuxDave

Originally posted by: McPhreak

Originally posted by: TuxDave
That proof looks good to me. I believe 0.9999... = 1. For those who don't believe still, show me 1-0.999... doesn't equal 0.

And if you say it equals 0.000000.....001... there's an infinite number of zeros, so that '1' never really exists, so technically 1-0.999... = 0

Does that mean 0.99999.....98 = 0.999999999.....99?

Ahh.. but there's a freaky difference. I say numbers like 0.9999....98 doesn't exist because we define there to be an infinite number of nines... and here with 0.9999...98 we say, there's a last nine, but there isn't.. there's infinite!

Well, that means 0.999999.... is infinitely smaller than 1.

Hence my latter question, is there such thing as a number that's infinitely smaller than 1. Because that implies that there exists a largest number smaller than 1. And I say no... such a number does not exist...

<edit>
just as there is no smallest number greater than 1. So since nothing can go between 0.999... and 1, AAND we say that there is no such largest number smaller than 1, we must conclude that they are equal.