New Proof that 1 = .999999999 Repeating

[nakedfrog]

Originally posted by: Bigsm00th
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:

I'm pretty sure it's already been settled. We're arguing apples and oranges. One argument is based on theory, and one on reality. Both statements are true. It equals 1 and it also does not equal 1.

 

[91TTZ]

Originally posted by: TuxDave
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.

In both questions, we're trying to measure a quantity.... a quantity which cannot be measured using our number system which was only meant to measure finite things.

The decimal system isn't cut out to do that stuff. It becomes a limitation of our numbering system.

In our numbering system, it's able to measure things in wholes, halfs, and tenths pretty efficiently. But things like thirds don't calculate so easily, the number will continue forever using the decimal system.

Also, simple things like circles are not measured easily by our system. A simple relationship such as the relationship between a circle's diameter and its circumference are not easy, round numbers. It should be, and we gave it a simple name, Pi, to symbolize this simple relationship, but using the decimal system that number doesn't work out. Do the calculation and it spews out an endless barrage of non-repeating numbers.

 

[dornick]

Originally posted by: 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.

well...actually... it is. .66R is not an approximation, it means the exact same thing as 2/3. What is a number? It's an idea, not a mark on paper or a computer screen. 2/3 and .66R are just different symbols for the same idea.

 

[MrDudeMan]

Originally posted by: nakedfrog

Originally posted by: Bigsm00th
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:

I'm pretty sure it's already been settled. We're arguing apples and oranges. One argument is based on theory, and one on reality. Both statements are true. It equals 1 and it also does not equal 1.

thats the thing...its a different way to say the same thing, so in theory and reality, it is exactly 1. ill be back in a little while...im going to go try to find the examples presented in a slideshow from a while back that clearly ends this thread and all discussion that disagrees with, mathematically and logically, .999.... = 1.

 

[nakedfrog]

Originally posted by: Bigsm00th

Originally posted by: nakedfrog

Originally posted by: Bigsm00th
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:

I'm pretty sure it's already been settled. We're arguing apples and oranges. One argument is based on theory, and one on reality. Both statements are true. It equals 1 and it also does not equal 1.

thats the thing...its a different way to say the same thing, so in theory and reality, it is exactly 1. ill be back in a little while...im going to go try to find the examples presented in a slideshow from a while back that clearly ends this thread and all discussion that disagrees with, mathematically and logically, .999.... = 1.

You go ahead and do that. This topic has been discussed ad nauseum, and "clearly ended" before, yet here it is again. It doesn't really matter in the long run, it's just so much mental masturbation.

 

[artikk]

Can you people just stop obsessing about things that are not important. 1=.999
There are a lot more crucial problems in the world without you blowing up this equation and mathematical fact out of proportion.

 

[MrDudeMan]

Originally posted by: nakedfrog

Originally posted by: Bigsm00th

Originally posted by: nakedfrog

Originally posted by: Bigsm00th
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:

I'm pretty sure it's already been settled. We're arguing apples and oranges. One argument is based on theory, and one on reality. Both statements are true. It equals 1 and it also does not equal 1.

thats the thing...its a different way to say the same thing, so in theory and reality, it is exactly 1. ill be back in a little while...im going to go try to find the examples presented in a slideshow from a while back that clearly ends this thread and all discussion that disagrees with, mathematically and logically, .999.... = 1.

You go ahead and do that. This topic has been discussed ad nauseum, and "clearly ended" before, yet here it is again. It doesn't really matter in the long run, it's just so much mental masturbation.

thats about the quality of reply i expected. there seems to be a clear division in the type of people in this debate. people with no prior mathematical knowledge or insanely large pride complexes have an issue with .999... = 1, which basically makes them troll in the thread, while the exact opposite types of people are on the other side of the fence. interesting observation IMO.

 

[nakedfrog]

Originally posted by: Bigsm00th

Originally posted by: nakedfrog
You go ahead and do that. This topic has been discussed ad nauseum, and "clearly ended" before, yet here it is again. It doesn't really matter in the long run, it's just so much mental masturbation.

thats about the quality of reply i expected. there seems to be a clear division in the type of people in this debate. people with no prior mathematical knowledge or insanely large pride complexes have an issue with .999... = 1, which basically makes them troll in the thread, while the exact opposite types of people are on the other side of the fence. interesting observation IMO.

:roll:
I don't think you read my post well enough. I've bolded the really important part of it for you. Here's a for your quality reply. Oh, and saying that there's people that agree with you, and people that are wrong isn't really an interesting observation.

 

[MrDudeMan]

Originally posted by: nakedfrog

Originally posted by: Bigsm00th

Originally posted by: nakedfrog
You go ahead and do that. This topic has been discussed ad nauseum, and "clearly ended" before, yet here it is again. It doesn't really matter in the long run, it's just so much mental masturbation.

thats about the quality of reply i expected. there seems to be a clear division in the type of people in this debate. people with no prior mathematical knowledge or insanely large pride complexes have an issue with .999... = 1, which basically makes them troll in the thread, while the exact opposite types of people are on the other side of the fence. interesting observation IMO.

:roll:
I don't think you read my post well enough. I've bolded the really important part of it for you. Here's a for your quality reply. Oh, and saying that there's people that agree with you, and people that are wrong isn't really an interesting observation.

i agree that it doesnt matter in the long run.

saying there are people that agree with you and then others that are wrong doesnt typically work, but in this situation it does because there is clearly a true answer to the problem. its a problem of mathematics, and those of us that claim to know better than mathematics are simply ignorant to facts and logic (ironically).

 

[91TTZ]

Originally posted by: Bigsm00th

thats about the quality of reply i expected. there seems to be a clear division in the type of people in this debate. people with no prior mathematical knowledge or insanely large pride complexes have an issue with .999... = 1, which basically makes them troll in the thread, while the exact opposite types of people are on the other side of the fence. interesting observation IMO.

That sounds like an overly elaborate way of saying "Those that agree with me are smart, while those that disagree with me are dumb".

 

[MAME]

Originally posted by: edro13
You people are absolutely retarded. EVERY SINGLE .999=1 equation is based on approximation and/or rounding up. Numbers are infinite, therefore, you can ALWAYS have a larger (or small) number, therefore, .99999~ can NEVER be = 1.

No matter what number you give me, I can always add another 9 on the end, making it not equal 1.

Yes, I understand what infinity is and that you cannot add a number to infinity because it is infinite... So in math, .999...==1, but in logic, .999... =/=1.

that's nice, so these PROOFS that mathematicians with PhD's put together are wrong? You do know what a proof is don't you? Have you ever bothered talking to someone who was an expert in the field about the subject?

 

[91TTZ]

Interesting link:

http://descmath.com/diag/nines.html

 

[Taejin]

Originally posted by: venk
The difference between 1 and .9 is 1/10 or .1
The difference between 1 and .99 is 1/100 or .01
The difference between 1 and .999 is 1/1000 or .001

Therefore


The difference between 1 and .99999 Repeating is 1/infinity or 0

Therefore 1 = .99999 Repeating


CLIFFS
--------------
1-.9 = .1
1 - .99 = .01
1- .999 = .001
1 - .9999 Repeating = 0

Not a very good proof.

 

[MrDudeMan]

Originally posted by: 91TTZ

Originally posted by: Bigsm00th

thats about the quality of reply i expected. there seems to be a clear division in the type of people in this debate. people with no prior mathematical knowledge or insanely large pride complexes have an issue with .999... = 1, which basically makes them troll in the thread, while the exact opposite types of people are on the other side of the fence. interesting observation IMO.

That sounds like an overly elaborate way of saying "Those that agree with me are smart, while those that disagree with me are dumb".

i didnt mean it like that though. dont read into it that much.

 

[91TTZ]

Here's a thought-

1 = 1

.999... = 1 - (1/infinity)

Since 1/infinity is a number, no matter how infinitely small, we can therefore say that 1- (1/infinity) is slightly less than 1, coming up short by an infinitely small margin.

Therefore, .9999... does not equal 1

 

[nakedfrog]

Originally posted by: 91TTZ
Interesting link:

http://descmath.com/diag/nines.html

:thumbsup:
I think that covers it all pretty well.

 

[Howard]

http://mathforum.org/library/drmath/view/53387.html

Given that a geometric series has a sum of a/(1-r) where a is the first term and r is the common ratio between terms, 0.9... has a = 0.9 and r = 1/10 (each successive .9 is ten times less than the previous), (9/10)/[1-(9/10)] = 1.

 

[91TTZ]

Originally posted by: Howard
http://mathforum.org/library/drmath/view/53387.html

Given that a geometric series has a sum of a/(1-r) where a is the first term and r is the common ratio between terms, 0.9... has a = 0.9 and r = 1/10 (each successive .9 is ten times less than the previous), (9/10)/[1-(9/10)] = 1.

You could also say since each successive placeholder is filled with a 9 instead of 1 on the previous placeholder, it must always come up short.

 

[Bassyhead]

not again

 

[dornick]

Originally posted by: 91TTZ
Interesting link:

http://descmath.com/diag/nines.html

Classic exmaple of a guy who knows just enough to be dangerous. You can tell he doesn't know what he's talking about when he uses language like "essentially the same quantity". Give me a break.

edit: read what Dr. Math says instead

 

[MrDudeMan]

Originally posted by: dornick

Originally posted by: 91TTZ
Interesting link:

http://descmath.com/diag/nines.html

Classic exmaple of a guy who knows just enough to be dangerous. You can tell he doesn't know what he's talking about when he uses language like "essentially the same quantity". Give me a break.

:thumbsup:

 

[91TTZ]

In the base-10 (decimal) system, each successive placeholder is 1/10th the value of the previous placeholder. Starting with the first place on the left side of the decimal point, you input its value. If you have 10, then the previous placeholder gets a "1".

9 falls short of 10
99 falls short of 100
999 falls short of 1000
9999 falls short of 10,000

In each of these cases, had the number been 1 larger, the placeholders would not have been filled with 9's... they'd have an extra placeholder added on the left, which would be filled with a 1, with the remaining digits becoming zeros.

Likewise,

0.9 falls short of 1.0
0.99 falls short of 1.00
0.999 falls short of 1.000
0.9999 falls short of 1.0000

In each of these cases, as you increase the amount of decimal places, the amount that it falls short by decreases by 1/10th. But the fact remains that it must have fallen short... otherwise you wouldn't be putting a "9" in the successive placeholder, you'd be putting a "1" in the previous placeholder.

The fact that you have repeating 9's tells you that you've fallen short. Since the number of 9's is infinite, you have missed by an infinitely small margin, but nevertheless, you have missed.

 

[dornick]

You're completely correct up until that last sentence. What do you mean by fallen short? You mean that one value is less than an other. The is not true of the 9 decimal series. Besides, you can't compare infinity to normal, everyday numbers.

Have you taken calculus yet? Back in the day, my reasoning was identical to yours, until I took calculus and realized I was wrong. If you haven't gotten there, trust us and you'll see If you still won't let it go, I recommend that Dr. Math link I put in my edit.

 

[91TTZ]

Originally posted by: dornick
You're completely correct up until that last sentence. What do you mean by fallen short?

Have you taken calculus yet? Back in the day, my reasoning was identical to yours, until I took calculus and realized I was wrong. If you haven't gotten there, trust us and you'll see If you still won't let it go, I recommend that Dr. Math link I put in my edit.

I'm saying that a given number will always be smaller than a number that has a larger value in the previous (leftward) placeholder.

Some fields in math must go an an assumption. Otherwise they won't work. They may be right 99.999R% of the time but they won't be right 100% of the time. Take Newtonian physics for example. Nobody would have thought that as you increase in speed the laws of physics can begin to follow other principles. But Einstein formulated that as you approach the speed of light, you gain mass.

 

[Rock Hydra]

Infinity is a variable, therefore it cannot be assigned a numeric value.