Definite proof that most of Digg readers are idiots

[UNCjigga]

So who cares if it is or it isn't?? What will YOU do with the knowledge either way?? Let me put it this way:

1. 1 = 0.99999999... -OR- 1 != 0.99999999...
2. ...
3. Profit?

So what comes next?

 

[halik]

Originally posted by: Dumac

Originally posted by: Kyteland

Originally posted by: KarmaPolice
Limits....wouldnt .9999999 repeating be appraoching 1?

No, .99.... is a concrete number with an exact value. It doesn't approach anything. That's like asking if 2/3 approaches 4/6, or if 3 approaches pi. However, there are number of functions that define 0.99.... that do approach 1 the closer you get to infinity, like the sum of 9/10^x. Similarly, the sum 1-1/3+1/5-1/7+1/9... approaces pi/4 when taken to a large number of steps. When evaluated at infinity it is exactly pi/4.

The sum of 9/10^x is exactly equal to 1 when taken to infinity.

No. .99... isn't a exact value. It repeats infinately. It is like saying 9/10 + 9/100 + 9/1000 and so on. It never ends, but keeps on APPROACHING one. It becomes so close to one that it is arguably ok to ignore the diffference, but it is definately not the exact same number as 1.

hahaha we have a digg reader onboard!

 

[Dumac]

Originally posted by: halik

Originally posted by: Dumac

Originally posted by: Kyteland

Originally posted by: KarmaPolice
Limits....wouldnt .9999999 repeating be appraoching 1?

No, .99.... is a concrete number with an exact value. It doesn't approach anything. That's like asking if 2/3 approaches 4/6, or if 3 approaches pi. However, there are number of functions that define 0.99.... that do approach 1 the closer you get to infinity, like the sum of 9/10^x. Similarly, the sum 1-1/3+1/5-1/7+1/9... approaces pi/4 when taken to a large number of steps. When evaluated at infinity it is exactly pi/4.

The sum of 9/10^x is exactly equal to 1 when taken to infinity.

No. .99... isn't a exact value. It repeats infinately. It is like saying 9/10 + 9/100 + 9/1000 and so on. It never ends, but keeps on APPROACHING one. It becomes so close to one that it is arguably ok to ignore the diffference, but it is definately not the exact same number as 1.

hahaha we have a digg reader onboard!

I know you were remarking on my supposed stupidity, but I actually haven't ever heard of digg.

 

[Minjin]

Originally posted by: BD2003

Originally posted by: PottedMeat
heh not reading the original thread, does this have any practical application?

Does it have to have one?

Einsteins theories had no practical applications at the time.

You guys wouldn't be able to communicate via these crazy machines we call computers if it wasn't for "geeks" who sat around and thought about stuff like this.

Mark

 

[cirthix]

Originally posted by: Kyteland

Originally posted by: fitzov

Originally posted by: KarmaPolice
Hrmmm its been a while since I took calc...answer a question for me...

Limits....wouldnt .9999999 repeating be appraoching 1?

I am not going to try to say they are wrong...they are math people..i suck at math...but wondering.

it approaches 1--it is not equal to 1. the only way I can think of (besides a simple logical proof) to prove it is by showing a graph of two functions--one whose range will go from .9 and approach 1 as it's domain increases while the other has a range of 1 for any domain.

0.99... isn't a function, it is a concrete number. Its value doesn't fluctuate over time. There are functions that exist that approximate this number, and when taken to infinity they are exactly equal, but only when taken to infinty. The sum of 9/10^x approaches 1 as you increase x, but that function doesn't define 0.99... unless x is infinity. When x=infinty, the value of that function is 1.

0.99... is not a defined number, it is essentially the limit as n->infinity of the sum 9/(10^n)

 

[Mathlete]

Originally posted by: mwtgg

Originally posted by: Unheard
.9repeating != 1

Take Calculus.

Why? This can be proven using simple HS algebra 1

Let x=0.999repeating

then 10x=9.99repeating (multiplicative property of equality and substitution)
and
10x=9.99999
- x=0.999999
9x=9

x=1(divide by 9)

QED

 

[KarmaPolice]

Thats what I was thinking..its not a exact number if it repeats forever.

I see corret stuff on both sides...

THe big issue with me is that...if it goes on forever...as .999repeating supposedly does...from the simple stand point of alawys adding a 9 on the end...it will never become 1. I thought that as close as they might be....even off by such a fraction we have no chance of ever seeing it..it still actually isnt one...

.9999999999999999999999999999999999999999999999999 is really close to 1...but its not..but if we say it repeats forever..then it is?


the on arguemtn that is interesting is the one that says there is no number x between 1 and .9999 repeating......this is true i suppose...but it keeps adding 9 at the end forever...ugh..

i dont like math...

 

[jagec]

Originally posted by: fitzov

Originally posted by: KarmaPolice
Hrmmm its been a while since I took calc...answer a question for me...

Limits....wouldnt .9999999 repeating be appraoching 1?


I am not going to try to say they are wrong...they are math people..i suck at math...but wondering.

it approaches 1--it is not equal to 1. the only way I can think of (besides a simple logical proof) to prove it is by showing a graph of two functions--one whose range will go from .9 and approach 1 as it's domain increases while the other has a range of 1 for any domain.

A simple logical proof? LOL! .99... = 1, and that's that. It only "approaches" one if it has a finite number of 9's after the decimal, with more being added all the time. The full number is equal to one.

The only infinitely small number is zero, sort of like the only infinitely large "number" is infinity. In other words, infinity -1, infinity, and infinity+1 have the SAME value. That's the basis of the 10x - x proof for .9999....=1.

I think part of the confusion comes from the word "infinitesimal", which in the vernacular is NOT the same as "infinitely small" in mathematics.

Originally posted by: KarmaPolice
THe big issue with me is that...if it goes on forever...as .999repeating supposedly does...from the simple stand point of alawys adding a 9 on the end...it will never become 1. I thought that as close as they might be....even off by such a fraction we have no chance of ever seeing it..it still actually isnt one...

.9999999999999999999999999999999999999999999999999 is really close to 1...but its not..but if we say it repeats forever..then it is?

Because there's an infinite number of 9's, you can add one to the end, or take one off, and the "number" of 9's doesn't change. The number still has the same value. Such is the nature of infinity.

 

[Kyteland]

Originally posted by: cirthix
0.99... is not a defined number, it is essentially the limit as n->infinity of the sum 9/(10^n)

That sum is simply a way of representing the number, but that isn't the number itself. What you are claiming is that a decimal representation of a number isn't an actual number. I hate to break it to you, but 0.33... is a number and it is exactly equal to 1/3. 0.500.. is a number and it is exactly equal to 1/2. 3.141592652...is a number and it is exactly equal to pi. Just because you are incapable of writing those numbers "exactly" on a sheet of paper doesn't mean that they don't exist.

And don't tell me that you can write 1/2 as 0.5 and leave it at that. 0 is a digit, and the decimal representation of 1/2 has an infinite number of them trailing it. Just because you have been conditioned to ignore them doesn't mean that they aren't there. Shortcuts aren't allowed.

0.99... is a defined number, as much as 0.33... and 1/2 are. If you want to deny the existence of decimal representation of numbers, that's your problem. If so 1/2 can't exist, because that's really 1.00.../2.0..., neither of which exist. I think the universe just imploded in a gigantic logical fallicy. 😉

 

[fitzov]

Originally posted by: Kyteland

Originally posted by: fitzov

Originally posted by: KarmaPolice
Hrmmm its been a while since I took calc...answer a question for me...

Limits....wouldnt .9999999 repeating be appraoching 1?

I am not going to try to say they are wrong...they are math people..i suck at math...but wondering.

it approaches 1--it is not equal to 1. the only way I can think of (besides a simple logical proof) to prove it is by showing a graph of two functions--one whose range will go from .9 and approach 1 as it's domain increases while the other has a range of 1 for any domain.

0.99... isn't a function, it is a concrete number. Its value doesn't fluctuate over time. There are functions that exist that approximate this number, and when taken to infinity they are exactly equal, but only when taken to infinty. The sum of 9/10^x approaches 1 as you increase x, but that function doesn't define 0.99... unless x is infinity. When x=infinty, the value of that function is 1.

0.99...isn't a function but a hyperreal number that is "infinitely close" to 1. the simple fact that 1 is a real number should be enough to show that .999... does not equal 1 (from a logical point of view).

 

[ruffilb]

Originally posted by: MathMan

Originally posted by: Unheard
.9repeating != 1

Wrong.

 

[QED]

Heh... all of this math talk is talk is getting me all hot and bothered.

😛

 

[Kyteland]

Originally posted by: KarmaPolice
Thats what I was thinking..its not a exact number if it repeats forever.

I see corret stuff on both sides...

THe big issue with me is that...if it goes on forever...as .999repeating supposedly does...from the simple stand point of alawys adding a 9 on the end...it will never become 1. I thought that as close as they might be....even off by such a fraction we have no chance of ever seeing it..it still actually isnt one...

.9999999999999999999999999999999999999999999999999 is really close to 1...but its not..but if we say it repeats forever..then it is?


the on arguemtn that is interesting is the one that says there is no number x between 1 and .9999 repeating......this is true i suppose...but it keeps adding 9 at the end forever...ugh..

i dont like math...

The part you're missing is that if you need to add 9's on to the end, the number you have is not 0.99... That number already has an infinite number of 9's. If you have to add anything to the end then you are simply approximating the number. Sure, if you take 0.9 and keep adding 9's to the end, that process will approximate 0.99... and will approach 1. The problem is that at no point during that process do you have anything that is actually 0.99... That process only approaches 0.99....

When you wrap your head around the fact that it both approaches 0.99... and 1 then you will see why they are equal.

 

[Kyteland]

Originally posted by: fitzov
0.99...isn't a function but a hyperreal number that is "infinitely close" to 1. the simple fact that 1 is a real number should be enough to show that .999... does not equal 1 (from a logical point of view).

Ugh, you know what? I'm not getting sucked in to this conversation again. I have work to do. We've had it before and all of these arguments have been hashed out. You're free to go read the thread. All 4000+ posts of it.

http://forums.anandtech.com/messageview.aspx?catid=38&threadid=954453&arctab=y

Come back when you're finished reading and let me know if you have anything new to add. I'll gladly have this debate with you then. I won't be so busy a month from now. 😛

 

[chuckywang]

Originally posted by: Unheard
.9repeating != 1

And you're an idiot.

 

[chambersc]

Originally posted by: Unheard
.9repeating != 1

seriously, rofl, why do people not get this. based off emperical observations i can categorically say .999 isn't 1.

 

[Born2bwire]

Oh boy, and this topic had stellar results here on Anandtech too. Hell, I got an idea, let's ask /. if the plane takes off... I need to stop coming into these threads, it just destroys my belief in humanity.

EDIT: Oh Jesus, more people said no in the poll than yes...

 

[QED]

Originally posted by: fitzov

Originally posted by: Kyteland

Originally posted by: fitzov

Originally posted by: KarmaPolice
Hrmmm its been a while since I took calc...answer a question for me...

Limits....wouldnt .9999999 repeating be appraoching 1?

I am not going to try to say they are wrong...they are math people..i suck at math...but wondering.

it approaches 1--it is not equal to 1. the only way I can think of (besides a simple logical proof) to prove it is by showing a graph of two functions--one whose range will go from .9 and approach 1 as it's domain increases while the other has a range of 1 for any domain.

0.99... isn't a function, it is a concrete number. Its value doesn't fluctuate over time. There are functions that exist that approximate this number, and when taken to infinity they are exactly equal, but only when taken to infinty. The sum of 9/10^x approaches 1 as you increase x, but that function doesn't define 0.99... unless x is infinity. When x=infinty, the value of that function is 1.

0.99...isn't a function but a hyperreal number that is "infinitely close" to 1. the simple fact that 1 is a real number should be enough to show that .999... does not equal 1 (from a logical point of view).

That's fallacious logic-- using it, if I have an imaginary number ( 1 + 0 i), it cannot possibly also be a real number (1). But we know that 1 + 0i is the same exact thing as 1.

In fact, if you consider the sequence of numbers .9, .99, .999, .9999, etc.. it is easibly provable that this sequence converges. It is easily proven that the convergent is 1. It is also just as easily proven that the convergent is .99..... . Now either 1 and .9999... are distinct real numbers and therefore the sequence really doesn't converge (and hence we have a logical contradiction), or 1 and .99999.... are one and the same.

 

[BD2003]

Originally posted by: Minjin

Originally posted by: BD2003

Originally posted by: PottedMeat
heh not reading the original thread, does this have any practical application?

Does it have to have one?

Einsteins theories had no practical applications at the time.

You guys wouldn't be able to communicate via these crazy machines we call computers if it wasn't for "geeks" who sat around and thought about stuff like this.

Mark

Exactly. :thumbsup:

 

[QED]

Originally posted by: chambersc

Originally posted by: Unheard
.9repeating != 1

seriously, rofl, why do people not get this. based off emperical observations i can categorically say .999 isn't 1.

Of course it's obvious .999 isn't 1.

However .999...... IS 1. And if you don't get that, you better stick to law school....

 

[jagec]

Originally posted by: chambersc

Originally posted by: Unheard
.9repeating != 1

seriously, rofl, why do people not get this. based off emperical observations i can categorically say .999 isn't 1.

Empirical??

Wow, you're too much. Please, I beg of you: show me your microscope that is able to resolve the difference between .999... and 1. I'll give you my life's savings for that treat.

 

[LeiZaK]

Originally posted by: MathMan

Originally posted by: chambersc

Originally posted by: Unheard
.9repeating != 1

seriously, rofl, why do people not get this. based off emperical observations i can categorically say .999 isn't 1.

Of course it's obvious .999 isn't 1.

However .999...... IS 1. And if you don't get that, you better stick to law school....

I get it, I just don't agree with it.

 

[Howard]

AH I HOPE I NEVER ARGUE WITH ANYBODY LIKE THAT

 

[KarmaPolice]

Jeez its fine if you think .9999 repeating is 1....but there is no reason to call people idiots that dont fully understand it or look down on them in anyway...

 

[bootymac]

Warning: The Content in this Article is Under Review
Readers have reported that this story contains information that may not be accurate.

😀