Is 1 = 0.9999......

[ElFenix]

Originally posted by: BigPoppa
Bruce Lee < 0.999.... = 1 < Coke < Maxima

fixed!

 

[RossGr]

9 + .09 + .009 + ... doesn't actually EQUAL anything, however the LIMIT of this series is 1. Your summation doesn't equal anything as it's a progression. It's limiting value is 0.

Yet another, who did not understand the material presented in basic calculus. Have you ever heard of a Cauchy Sequence? The above sequence is a Cauchy Sequence and it does converge and it does equal the limit.

You people you think that for something to be equal in the limit mean that it is only approximately equal need to take some refresher courses. .999... is shorthand notation for the sum to infinity, not approaching infinity but INFINITY, therefore equality holds.


Spencer278,
So I show you that your sum is not .00...01, where the ellipsis is interpreted incorrectly to mean an infinite number of zeros and you still think you are correct. If you had meant 1 -.9*10^-n , I think you would have written that. I still see your original expression as a misguided effort to represent the none real expression of an infinite number of zeros followed by something.


To those who butt into this thread with go comment other then request its lock, why do you even open the thread? I do not butt into your inane YAGT, or any of your other teenage angst issues, so why must you crap on this one? Unless you are trying to keep it alive! Just leave it be, let it die its own death.

 

[Indolent]

Originally posted by: RossGr

To those who butt into this thread with go comment other then request its lock, why do you even open the thread? I do not butt into your inane YAGT, or any of your other teenage angst issues, so why must you crap on this one? Unless you are trying to keep it alive! Just leave it be, let it die its own death.

This thread will never die unless it is "accidently" deleted by a mod.

 

[cmaMath13]

I love it!

 

[MAME]

Spencer, I will refrain from calling you a moron but you just dispproved yourself:
you calim ".000...1 exsits and is equal to zero". Lets say that you, even though no math professor in the world agrees, proved that .000...1 exists. Now you claim it's equal to 0.

So basically you have .000...1 + .999... = 1. I'll substitute a 0 in for .000...1 and LOOKIE HERE!!!!!!! 0+.999... = 1 or .999...=1


Now lets say .000...1 doesn't exist (which it doesn't): can you tell me what to add to .999... to get to 1? That's what I thought.


Good lord man, you have lost, get over it. They are EXACTLY equal. If you still insist of making an ass of yourself, please disprove ANY of the proofs linked to in this thread. You simply stutter out crap form your mouth without proving anything.

 

[Spencer278]

Originally posted by: MAME
Spencer, I will refrain from calling you a moron but you just dispproved yourself:
you calim ".000...1 exsits and is equal to zero". Lets say that you, even though no math professor in the world agrees, proved that .000...1 exists. Now you claim it's equal to 0.

So basically you have .000...1 + .999... = 1. I'll substitute a 0 in for .000...1 and LOOKIE HERE!!!!!!! 0+.999... = 1 or .999...=1


Now lets say .000...1 doesn't exist (which it doesn't): can you tell me what to add to .999... to get to 1? That's what I thought.


Good lord man, you have lost, get over it. They are EXACTLY equal. If you still insist of making an ass of yourself, please disprove ANY of the proofs linked to in this thread. You simply stutter out crap form your mouth without proving anything.

My claim was that the prof above about .0000...1 not existing because then what would .0000...1/2 be was illogical because .0000...1 would be equal to .0000...1/2 and therefor the prof falls apart.

 

[conjur]

DIE, THREAD!! DIIIIIEEEEEEEEEEEE!!!!

 

[videoclone]

How on earth did a boring thread like this get this about of Replies .., Geeezzzzzz :Q

 

[MAME]

Originally posted by: Spencer278

Originally posted by: MAME
Spencer, I will refrain from calling you a moron but you just dispproved yourself:
you calim ".000...1 exsits and is equal to zero". Lets say that you, even though no math professor in the world agrees, proved that .000...1 exists. Now you claim it's equal to 0.

So basically you have .000...1 + .999... = 1. I'll substitute a 0 in for .000...1 and LOOKIE HERE!!!!!!! 0+.999... = 1 or .999...=1


Now lets say .000...1 doesn't exist (which it doesn't): can you tell me what to add to .999... to get to 1? That's what I thought.


Good lord man, you have lost, get over it. They are EXACTLY equal. If you still insist of making an ass of yourself, please disprove ANY of the proofs linked to in this thread. You simply stutter out crap form your mouth without proving anything.

My claim was that the prof above about .0000...1 not existing because then what would .0000...1/2 be was illogical because .0000...1 would be equal to .0000...1/2 and therefor the prof falls apart.

Thanks for totally ignoring my points. Fine, you magically disproved Mathematics and came up with .000...1 Now, since it's also equal to 0, you can agree that .999... = 1. Thanks so much

 

[conjur]

Originally posted by: conjur
DIE, THREAD!! DIIIIIEEEEEEEEEEEE!!!!

 

[MAME]

if you don't like the thread, DON'T CLICK ON IT

 

[onelin]

yes it is. Sad to see that a lot of people disagree The proof is 100% sound, 'nuff said.

Put .9 repeating and 1 on a numberline, do there exist any numbers between them? no. That's because they're the same number

I also did an extension on one once that, after proving 1/9th is .1 repeating, adding up 9 1/9th's to = 1 gives you .9 repeating for a little more logic.

 

[conjur]

Originally posted by: MAME
if you don't like the thread, DON'T CLICK ON IT

You guys are rehashing the same old arguments that comprise the first 8,247 posts in this thread.

 

[silverpig]

Originally posted by: Spencer278

Originally posted by: silverpig

Originally posted by: Spencer278

Originally posted by: RossGr

1 + sum( n = 0 to infinity )( -1.0 * 10^(-n) + 1.0 * 10^-(n+1) )= .000...1

LOL! NOT!

Refresh youself in basic exponetial arithematic!

10^-(n+1) - 10^(-n) = 10^-n ((10^-1) -1 ) = -.9*10^-n

for sum up to 0
1 + -1.0^(-0) + 1.0*10^-(0+1) = .1
upto 1
.1 + -1.0^(-1) + 1.0*10^-(1+1) = .01
upto 2
.01 + -1.0^(-2) + 1.0*10^-(2+1) = .001
I will let you finish the sum.

If you don't like the sum you could think of .000...1 as
1/1000...

You have a progression whose limiting value is zero.

.9 + .09 + .009 + ... doesn't actually EQUAL anything, however the LIMIT of this series is 1. Your summation doesn't equal anything as it's a progression. It's limiting value is 0.

So you agree that .000...1 exsits and is equal to zero?

So you agree unicorns exist?

 

[silverpig]

Originally posted by: RossGr

9 + .09 + .009 + ... doesn't actually EQUAL anything, however the LIMIT of this series is 1. Your summation doesn't equal anything as it's a progression. It's limiting value is 0.

Yet another, who did not understand the material presented in basic calculus. Have you ever heard of a Cauchy Sequence? The above sequence is a Cauchy Sequence and it does converge and it does equal the limit.

You people you think that for something to be equal in the limit mean that it is only approximately equal need to take some refresher courses. .999... is shorthand notation for the sum to infinity, not approaching infinity but INFINITY, therefore equality holds.


Spencer278,
So I show you that your sum is not .00...01, where the ellipsis is interpreted incorrectly to mean an infinite number of zeros and you still think you are correct. If you had meant 1 -.9*10^-n , I think you would have written that. I still see your original expression as a misguided effort to represent the none real expression of an infinite number of zeros followed by something.


To those who butt into this thread with go comment other then request its lock, why do you even open the thread? I do not butt into your inane YAGT, or any of your other teenage angst issues, so why must you crap on this one? Unless you are trying to keep it alive! Just leave it be, let it die its own death.

I just wrote down a bunch of numbers you add together; I didn't specify any summation over a range.

.9 + .09 + .009 + ... = Sum N{1,M} [9*.1^N] = B

This doesn't equal anything. For lim M->inf we have that this series converges to 1, but the sum as I wrote it doesn't actually equal any number.

 

[RossGr]

9 + .09 + .009 + ... = Sum N{1,M} [9*.1^N] = B

I disagree. you have presened a recognizable pattern followed by an ellipsis. This means I should continue the pattern infinitly. What you have represented is = .999... . The sum does not terminate at some unspecificed M, it continues to infinity.

 

[DrPizza]

Originally posted by: RossGr

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

Everyone who has gotten beyond Calculus and taken a Real Analysis Course know that it is equal to 1. Once again, .999... is a fixed number, it does not APPROACH anything, it is a fixed number, just like 1 does not approach anything.

I beg to differ. Everyone who has taken calculus should know that it is equal to one. Not that it approaches 1. It doesn't take beyond calculus. (I teach calc... sums of infinite geometric series are definitely covered.)

 

[Yax]

Originally posted by: DrPizza

Originally posted by: RossGr

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

Everyone who has gotten beyond Calculus and taken a Real Analysis Course know that it is equal to 1. Once again, .999... is a fixed number, it does not APPROACH anything, it is a fixed number, just like 1 does not approach anything.

I beg to differ. Everyone who has taken calculus should know that it is equal to one. Not that it approaches 1. It doesn't take beyond calculus. (I teach calc... sums of infinite geometric series are definitely covered.)

HA! I saw the proof in Algebra 2. Before Calculus so there.

 

[Yax]

Someday, the length of this thread will reach infinity. Then we will know the answer.

 

[mchammer187]

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

 

[Yax]

Originally posted by: mchammer187

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

You didn't understand calculus did you. You didn't do your plot right either, if you didn't get Y=1 for any X.

 

[bleeb]

Originally posted by: mchammer187

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

0.9999... != 1. There is not such thing as infinity... therefore 0.9999... != 1.

 

[MAME]

Originally posted by: bleeb

Originally posted by: mchammer187

Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

0.9999... != 1. There is not such thing as infinity... therefore 0.9999... != 1.

Are you thread crapping or just an idiot?

 

[MAME]

 

[Kyteland]

First off lets restate some points for clarity. If you disagree with any of this please speak up.

1) 0.9999.... is NOT a limit, sum, etc. The graph of f(x) = 0.9999... does not change value at any x along the graph. It has an exact value and that is 0.9999.... f(infinity) = f(0) = f(anything) = 0.9999.... (This statement is true whether or not 1=0.9999...)

2) The summation "Sum N{1,M} [9*.1^N] = B" is equal to 0.9999... ONLY when M is infinity. In this summation B approaches 1 on the graph as M increases. This graph, however, is NOT a graph of 0.9999..... (This statement is true whether or not 1=0.9999...)

3) "1 - Sum N{1,M} [10^(-N) - 10^(-N+1)] = B" is a valid summation for producing N zeros followed by a 1. When N=infinity this summation equals zero (<-- personal belief. Prove to me that it's not). If one was to make the assumption that infinite 0s followed by a 1 existed, then this is the way that you would construct it. I believe that when Spencer278 mentioned this he was simply using the "number" everyone else was using: 0.0000...1. Don't flame him because he used a concept somebody else invented.

4) "1 - Sum N{1,M} [10^(-N) - 10^(-N+1)] = B" resuces to "1 - Sum N{1,M} [9*.1^N]= B" when you add this to the summation for 0.9999.... you get "1 - Sum N{1,M} [9*.1^N] + Sum N{1,M} [9*.1^N]" = 1 (This statement is true whether or not 1=0.9999...)

I suppose the sticking point of all this is in 3). I personally believe that the summation equals 0 at infinity.

discuss....