New Proof that 1 = .999999999 Repeating

[frank84]

Originally posted by: silverpig

Originally posted by: 91TTZ
I still like my argument that .9999 repeating = the largest possible fraction less than 1. It misses being 1 by the smallest possible amount.

I know for all intents and purposes math considers .9999..... to be 1, so this is more of a logic/philosophy argument.

*sigh*

You're wrong. It's not philosophy, it's math. 1 = .999... and that is that.


This thread ends *now*

No it doesnt

 

[dornick]

Originally posted by: element

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

that's got to be the worst attempt at a proof I've ever seen.

No shit, that's why I didn't say it was a proof :disgust: I used to be convinced they were different too, then I got into calculus and learned about things like limits and infinite series

 

[oboeguy]

This thread (and teh last one) have lowered our IQs by how many points? Anyhow, unless you're one of those nutjobs into infinitesimals, 1 = 0.99... Period! So, in conclusion of this post and hopefully this thread, if you don't believe that 1 = 0.99... you are either

1) a no0b who can't "get" basic math

or

2) a crazy mathematician / logician with nothing better to do.

 

[edro]

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.

 

[Apathetic]

Oh God, not another one of these damn things.

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

WRONG

Dave

 

[SagaLore]

I say that we get a dedicated forum for this discussion.

 

[jalaram]

6 * 9 = 42

 

[JohnCU]

Everyone says wrong, and then does not say why. Then people say right, and I've taken advanced math classes, but they don't say why, either.

 

[vtqanh]

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.

Go read the other thread and report back to us, ok?

 

[nakedfrog]

Originally posted by: beer
No one - NO ONE - has provided even the slightest proof as to why .9999.... does not equal one. Meanwhile, those that contend that .99999 = 1 have provided at least a rough proof indicating why.

A logical person would believe the latter.

No, a logical person would believe since you can clearly see that 1 != 0.999..., they are in fact not equal to each other. It may make people feel good to use proofs to say that they are equal, but for all practical purposes they are not equal and shall continue to be not equal.

 

[xospec1alk]

is this P&N?

 

[dornick]

When was the last time you used .999... for a practical purpose? You're basing your assumption that they're different simply because they look different. Nevertheless, in math AND logic, they are simply two different symbols for the same idea. I seem to recall some theorm that says you can always find a seperate number between two other distinct numbers.

So show me a number between .999... and 1 and I'll concede that they are different

 

[dragonballgtz]

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

:thumbsdown:

 

[nCred]

Originally posted by: nakedfrog

Originally posted by: beer
No one - NO ONE - has provided even the slightest proof as to why .9999.... does not equal one. Meanwhile, those that contend that .99999 = 1 have provided at least a rough proof indicating why.

A logical person would believe the latter.

No, a logical person would believe since you can clearly see that 1 != 0.999..., they are in fact not equal to each other. It may make people feel good to use proofs to say that they are equal, but for all practical purposes they are not equal and shall continue to be not equal.

No, For all PRACTICAL purposes they are equal.

 

[FreshFish]

1/infinity != 0
1/infintiy approaches 0

 

[dornick]

1/infinity doesn't make sense, as infinity is not a number

what you mean is: lim (n->infinity) 1/n = 0

 

[edro]

Originally posted by: vtqanh

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.

Go read the other thread and report back to us, ok?

I have ALL 53249248 of the .999... threads... I just thought I would sum it up.

 

[Argo]

Why is the difference between 1 and 0.99999... = 1/infinity? Where did you get infinity from?

 

[DanTMWTMP]

geezes..

Every math professor will tell you 0.9999~infinity is 1. infinity is forever. There is no 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.
Just learn some basic laws of sequencing numbers, and this concept is very very easy to understand.

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.

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.

((edited for repeating myself 100 times ))

 

[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.

 

[edro]

Originally posted by: DanTMWTMP
geezes..

Every math professor will tell you 0.9999~infinity is 1. infinity is forever. There is no 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.
Just learn some basic laws of sequencing numbers, and this concept is very very easy to understand.

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.

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.

((edited for repeating myself 100 times ))

:thumbsup:

 

[nakedfrog]

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.

Well there you go. Logical people say .9999 != 1 because we're talking about numbers. Since that's what we actually use in day to day life, and not abstract mathematical concepts, they are correct in saying that .99999 != 1. However, that does not invalidate the mathematical proof that .99999 = 1.
So, in closing
.999999999 = 1
and
.999999999 != 1

 

1 = 1 in my world.

 

[Tifababy]

In 6th grade, I was taught this proof:

x=.999...
10x = 9.999...
subtract the two:
9x=9
therefore x=1

Seems like a simple proof to me.

 

[KevinF]

Originally posted by: nakedfrog

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.

Well there you go. Logical people say .9999 != 1 because we're talking about numbers. Since that's what we actually use in day to day life, and not abstract mathematical concepts, they are correct in saying that .99999 != 1. However, that does not invalidate the mathematical proof that .99999 = 1.
So, in closing
.999999999 = 1
and
.999999999 != 1

Exactly. However, the real issue is that .999999999999=1 only in the real number system. People's intuitive understanding that .999999999999 is just a tiny bit smaller than 1 only works in the hyperreal number system, the system developed to provide mathematical rigor to calculus with infinitesimals.