New Proof that 1 = .999999999 Repeating

[bigredguy]

see sig

 

[mchammer187]

Originally posted by: vtqanh

Originally posted by: DanTMWTMP
geezes..

Every math professor will tell you 0.9999~infinity is 1. infinity is forever. There is not stop.

0.999999~ is a sequence. the official value of the number is the limit
of the sequence of these numbers that gets closer to its limit. 0.99999's limit is 1.

0.999999~ infinity DOESN'T STOP. there's no "oh I can add one more 9, it still won't be 1." umm.

no.

IT's not about adding more 9's, and it's not about logic. well, actually, in computer logic, 0.9999~ is 1. Rudimentary human logic HAS NOTHING TO DO WITH this.
This. Is. Math. infinity doesn't stop. it goes on forever, and there's no way you can "add" more digits to an already sequencing number that goes on forever. That's just not possible.

no logic, no philosophy, just math. 0.9999~ = 1 is not a subject about logic nor philosophy, it's a subject of math where THERE IS ONLY A SET OF SOLUTIONS. in this case, 0.9999~ 's only solution is that it equals to 1.

winnar!
Most people come to this discussion with the idea of 0.99999~ being a number, that's when everything goes wrong.

.999~ is not a sequence

.9999~ is a number

if you plot it on a cartesian plane it is a completely horizontal line (ie a number)
it does not approach anything, and it holds the same value at x = negative infiniti to x = infiniti

there is no limit to .99~

it is equal to 1

if you are talking about .9 + .09 + .009 + .0009... then we have a series

whose sum converges to 1,

.99999...... is the sum of the series, therefore .9999.... = 1

the major point people fail to grasp is

1 - .99999999.......

people will argue that this equals .0000.........1

even a basic understanding of infiniti should tell you that such a number cannot exist

if there was that dangling 1 at the end then the infinitely repeating decimal is infact not infinitely repeating


think about it this way, thats like saying something is at the end of an infinitely long highway

if there is something at the end than obviously it ends, therefore it is not infinitely long

 

[silverpig]

Originally posted by: mchammer187


.999~ is not a sequence

.9999~ is a number

if you plot it on a cartesian plane it is a completely horizontal number
it does not approach anything, and it holds the same value at x = negative infiniti to x = infiniti

there is no limit to .99~

it is equal to 1

if you are talking about .9 + .09 + .009 + .0009... then we have a series

whose sum converges to 1,

.99999...... is the sum of the series, therefore .9999 = 1

the major point people fail to grasp is

1 - .99999999.......

people will argue that this equals .0000.........1

even a basic understanding of infiniti should tell you that such a number cannot exist

if there was that dangling 1 at the end then the infinitely repeating decimal is infact not infinitely repeating


think about it this way, thats like saying something is at the end of an infinitely long highway

if there is something at the end than obviously it ends, therefore it is not infinitely long

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

 

[nakedfrog]

Originally posted by: silverpig

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

That's different, because there's obviously work to be performed on one side of 1 + 1 = 2. Not so with .999999 = 1, because that shows that no work needs to be done.
Does .999999 + .999999 = 2?

 

[HomerJS]

Isn't this how programmers years ago used to rip off banks?

 

[nCred]

Originally posted by: nakedfrog

Originally posted by: silverpig

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

That's different, because there's obviously work to be performed on one side of 1 + 1 = 2. Not so with .999999 = 1, because that shows that no work needs to be done.
Does .999999 + .999999 = 2?

1.999... = 2?

 

[DrPizza]

Originally posted by: nCred

Originally posted by: nakedfrog

Originally posted by: silverpig

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

That's different, because there's obviously work to be performed on one side of 1 + 1 = 2. Not so with .999999 = 1, because that shows that no work needs to be done.
Does .999999 + .999999 = 2?

1.999... = 2?

Yes.
exactly 2.

I'm wondering how many people here think that .3333333... (repeating forever) is less than 1/3. On the number line, it's in the *EXACT SAME SPOT* as 1/3. Think about that for a little while.

 

[silverpig]

Originally posted by: nakedfrog

Originally posted by: silverpig

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

That's different, because there's obviously work to be performed on one side of 1 + 1 = 2. Not so with .999999 = 1, because that shows that no work needs to be done.
Does .999999 + .999999 = 2?

You're making it up as you go along now. They are both representations of the same value.

 

[eLiu]

while the statement is true, your proof sucks

 

[Darien]

Originally posted by: HomerJS
Isn't this how programmers years ago used to rip off banks?

Office Space?

 

[element]

Originally posted by: DrPizza

Originally posted by: nCred

Originally posted by: nakedfrog

Originally posted by: silverpig

:beer:

Thanks. Saved me from typing.

Also: To those of you who say 0.999... < 1 because they are not "the same" then pray tell, does 1 + 1 != 2? They sure don't look the same to me. What about VI and 6?

That's different, because there's obviously work to be performed on one side of 1 + 1 = 2. Not so with .999999 = 1, because that shows that no work needs to be done.
Does .999999 + .999999 = 2?

1.999... = 2?

Yes.
exactly 2.

I'm wondering how many people here think that .3333333... (repeating forever) is less than 1/3. On the number line, it's in the *EXACT SAME SPOT* as 1/3. Think about that for a little while.

yuo aere so reatarded!!!!oneoneoneon0.999...0.999...
0.333..does nots the equals too 1/3 it approweaches ittts!!!!1111oneone0.999...0.999...



just kiddin!:laugh:

ok seriously what happens when you subtract 0.999... from 1?
1-0.999...= what? 0.0001? nope 0.000000001? no...that last 1 never gets written! that's the meaning of infinity. get it or forever be a numbskull

note also that when you forget to press the shift key when typing out the exclamation point 0.999... appeared up there. so that's proof 0.999...=1

:laugh::laugh::laugh::laugh::laugh::laugh::laugh::laugh::laugh::laugh:

 

[Tom]

Originally posted by: dornick
this is hilarious. .9R IS equal to one. It's the advanced math classes that let you realize this. But for all you high school kids out there...

1/3 = .33R
+ 2/3 = .66R
---------------
3/3 = .99R = 1

Not mathematical at all, but gets the point across

2/3 doesn't equal .66R.

.66R is an approximation, not a number.

2/3 is a number.

1 is a number

.99... or .99R or .99~whatever, are not numbers.

 

[yoda291]

For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

 

[Jfrag Teh Foul]

These threads=.repost~infinity

 

[91TTZ]

Originally posted by: yoda291
For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

No, in logic they'd say that 1 = 1, and therefore .9999R can't equal one. If it was one, they'd call it one, and not a huge fraction.

The reason is the simple fact that 1 has a whole number on the left side of the decimal point, whereas .9999R has an infinite amount of numbers on the RIGHT side of the decimal meaning it's a fraction. An infinitely large fraction, yes. But it still misses being a whole number by an infinitely small amount.

 

[gabemcg]

42

 

[TuxDave]

Originally posted by: 91TTZ

Originally posted by: yoda291
For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

No, in logic they'd say that 1 = 1, and therefore .9999R can't equal one. If it was one, they'd call it one, and not a huge fraction.

The reason is the simple fact that 1 has a whole number on the left side of the decimal point, whereas .9999R has an infinite amount of numbers on the RIGHT side of the decimal meaning it's a fraction. An infinitely large fraction, yes. But it still misses being a whole number by an infinitely small amount.

Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

 

[91TTZ]

Let me pose another similar scenario:

Space is infinite.

Let's say you have 2 identical space probes out in the middle of space. They're travelling the same speed and in the same direction. But you released one of the probes a second before you released the other. Which one is in further along in its journey? If there's no reference point to compare it to a solid, absolute point, how can you say which one is further along? You could only tell where one is in reference to the other one, but when talking about the big picture they're just in the middle of an infinite voyage. Neither one is closer or further from the beginning or the end of space, since it's infinite. For all the probes know, they're sitting still, a few feet apart. One you lose sight of every other point of reference, you become your only point of reference.

 

[91TTZ]

Originally posted by: TuxDave


Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

1 over 0.999....

(1/0.999...)

 

[TuxDave]

Originally posted by: 91TTZ
Let me pose another similar scenario:

Space is infinite.

Let's say you have 2 identical space probes out in the middle of space. They're travelling the same speed and in the same direction. But you released one of the probes a second before you released the other. Which one is in further along in its journey? If there's no reference point to compare it to a solid, absolute value, how can you say which one is further along? You could only tell where one is in reference to the other one, but when talking about the big picture they're just in the middle of an infinite voyage. Neither one is closer or further from the beginning or the end of space, since it's infinite.

I don't see how this is anything related to the 0.999... question. You can claim the first one is 'ahead' of the second one merely by the observation that there's physically a distance between them and that in the defined 'forward direction', the first one is leading the other.

 

[TuxDave]

Originally posted by: 91TTZ

Originally posted by: TuxDave


Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

1 over 0.999....

(1/0.999...)

uh.... I'm guessing you really mean 0.999.... /1? Otherwise since you claim 0.9999 < 1 (I'm guessing), 1/0.999... would be greater than 1.

 

[nakedfrog]

Originally posted by: TuxDave

Originally posted by: 91TTZ

Originally posted by: yoda291
For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

No, in logic they'd say that 1 = 1, and therefore .9999R can't equal one. If it was one, they'd call it one, and not a huge fraction.

The reason is the simple fact that 1 has a whole number on the left side of the decimal point, whereas .9999R has an infinite amount of numbers on the RIGHT side of the decimal meaning it's a fraction. An infinitely large fraction, yes. But it still misses being a whole number by an infinitely small amount.

Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

Whatever number it is that removes all the values behind the decimal point and places a value in front of the decimal point. What number that is is irrelevant, because if they were equal, they would both have the same value on both sides of the decimal point.

 

[MrDudeMan]

Originally posted by: TuxDave

Originally posted by: 91TTZ

Originally posted by: yoda291
For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

No, in logic they'd say that 1 = 1, and therefore .9999R can't equal one. If it was one, they'd call it one, and not a huge fraction.

The reason is the simple fact that 1 has a whole number on the left side of the decimal point, whereas .9999R has an infinite amount of numbers on the RIGHT side of the decimal meaning it's a fraction. An infinitely large fraction, yes. But it still misses being a whole number by an infinitely small amount.

Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

obviously .000001





i cant believe there are people who still dont know .999999... = 1. i mean its like they disagree with calculus. so do you guys pick and choose which parts of advanced math you choose to agree?

hey, lets argue that T = I*a doesnt equal F = M*a next...that will be fun! :roll:

 

[TuxDave]

Originally posted by: nakedfrog

Originally posted by: TuxDave

Originally posted by: 91TTZ

Originally posted by: yoda291
For the logic people.

If .9 repeating and 1 are not the same, then they must be different.
If I were comparing 2 and 4/2, I can say they are the same because there is no difference between the two of them. The difference is zero.
So then I ask what is the difference between .9r and 1? The answer is zero.

It's not an infinite series of zeroes followed by a one. It's zero. nada.nothing. I get the impression you think this number is constantly being built up somewhere. That at some point down the line, there's a short leprechaun sitting on the zillionth decimal spot watching the zeroes pile up until they catch up to him and that, maybe if you're really nice, he'll let you add that one. It's not true.
Logic should tell you that any number consisting of nothing but zeroes = 0.

No, in logic they'd say that 1 = 1, and therefore .9999R can't equal one. If it was one, they'd call it one, and not a huge fraction.

The reason is the simple fact that 1 has a whole number on the left side of the decimal point, whereas .9999R has an infinite amount of numbers on the RIGHT side of the decimal meaning it's a fraction. An infinitely large fraction, yes. But it still misses being a whole number by an infinitely small amount.

Assuming we both agree that the number system is continuous, if 0.999.... does not equal 1, there 'should' exist a number between the two. What is that number?

Whatever number it is that removes all the values behind the decimal point and places a value in front of the decimal point. What number that is is irrelevant, because if they were equal, they would both have the same value on both sides of the decimal point.

Explain on more time what that number is? I'm not looking for a transformation from 0.999... to 1. I'm not looking for a difference. There is no 'remove something such that something. What number on the number line exists between 0.999... and 1?

 

[MrDudeMan]

Originally posted by: TuxDave

Originally posted by: 91TTZ
Let me pose another similar scenario:

Space is infinite.

Let's say you have 2 identical space probes out in the middle of space. They're travelling the same speed and in the same direction. But you released one of the probes a second before you released the other. Which one is in further along in its journey? If there's no reference point to compare it to a solid, absolute value, how can you say which one is further along? You could only tell where one is in reference to the other one, but when talking about the big picture they're just in the middle of an infinite voyage. Neither one is closer or further from the beginning or the end of space, since it's infinite.

I don't see how this is anything related to the 0.999... question. You can claim the first one is 'ahead' of the second one merely by the observation that there's physically a distance between them and that in the defined 'forward direction', the first one is leading the other.

as long as you are in an inertial frame of refernce, it would be very clear which was ahead of the other. actually, even if the probes were spinning but still had the same linear speed in whatever direction they were headed, you could still very easily tell which was in front of the other.