.99999.... =1. No, really, it does.

[Flip217]

.9999999.... (repeating) is equal to 1. And here's the proof. (http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html)

.9 repeating equals one. In other words, .9999999... is the same number as 1. They're 2 different ways of writing the same number. Kind of like 1.5, 1 1/2, 3/2, and 99/66. All the same...

1/3=.33333333...
2/3=.66666666...
3/3=.99999999...

And 3/3=1, so .99999999....=1, too.

This kind of stuff makes my brain hurt.

Yay! Math!

[The Wedge]

Math forever lost me when the imaginary number i was introduced. I still remember that day vividly. I was always a little smartass, but that day it was coupled with pure confusion and derision as I began to question that poor teacher. These concepts couldn't work, so you had to create this imaginary number, a number THAT DOESN'T EXIST to make it work...why can't I make up stuff then in any of these problems? That was about the most basic thing I went with that day almost 20 years ago (ouch).

Then Big Bang Theory had an exchange that reminded me of how I felt that day:
Leonard: [discussing Sheldon's work] At least I didn't have to invent 26 dimensions to get the math to work.
Sheldon: I didn't invent them. They're there.
Leonard: Yeah? In what universe?
Sheldon: In all of them, that's the point!

[waroriole]

Makes sense. Sometimes I wish I had majored in math.

[JamesI]

Math forever lost me when the imaginary number i was introduced. I still remember that day vividly. I was always a little smartass, but that day it was coupled with pure confusion and derision as I began to question that poor teacher. These concepts couldn't work, so you had to create this imaginary number, a number THAT DOESN'T EXIST to make it work...why can't I make up stuff then in any of these problems? That was about the most basic thing I went with that day almost 20 years ago (ouch).


I took a graduate math class on imaginary numbers. It was actually the most interesting math course I ever took.

[Sanfran327]

I have a hard time buying this. If you take a small portion of any object away, you no longer have the whole object.

You have almost a whole object.

[The Epic]

In another forum, this led to an argument that got somebody banned. Seriously.

So I'm not going to go into detail because this will turn into a ten-page thread, but I completely disagree with the OP. It doesn't. It never will. It can't.

[The Wedge]

The main disconnect is in the fact that it's .9 *repeating*. In essence, that *repeating* means infinity, but it also has to be a finite fixed number...it's a paradoxical problem that ends up making in another paradox of .99999... = 1.

I still don't trust math.

[Dr. FLK]

There is no non-zero 'x' that satisfies |1-0.99999999....|>x. As soon as you truncate 0.999... to a finite number of digits, then an 'x' can be solved for. Infinity is a funny thing...

[waroriole]

I have a hard time buying this. If you take a small portion of any object away, you no longer have the whole object.

You have almost a whole object.

It's not hard to understand:

1/3= .333333 repeating
2/3= .666666 repeating

1/3 + 2/3 = 1, so .3333 repeating + .6666 repeating should equal 1.

[waroriole]

In another forum, this led to an argument that got somebody banned. Seriously.

So I'm not going to go into detail because this will turn into a ten-page thread, but I completely disagree with the OP. It doesn't. It never will. It can't.

Can you go into a little more detail as to why you think it's not true. I don't think we will get too worked up about a math equation on OH.

[TyCobb]

Can you go into a little more detail as to why you think it's not true. I don't think we will get too worked up about a math equation on OH.

He is wrong. It is a mathematical proof and a pretty easy one at that.

http://upload.wikimedia.org/math/5/6/9/56949181a290ce561f27bd550a720392.png

[RShack]

It's not hard to understand:

1/3= .333333 repeating
2/3= .666666 repeating

1/3 + 2/3 = 1, so .3333 repeating + .6666 repeating should equal 1.
But we don't deal with numbers that repeat forever. We always round them off. There are rules about how many digits of precision are appropriate, given other the factors of an equation.

.333333 is not the same as 1/3. It's an approximation of 1/3.
.666666 is not the same as 2/3. It's an approximation of 2/3.
Whenever you terminate it at X digits, you use rounding rules.
The rounding rules say that the approximation of 2/3 doesn't end in a 6, it ends in a 7.
So, .333333 + .333333 is not .666666, it's .666667.
Are you gonna claim that 3 + 3 = 7 ? I bet not...

So this is a just a theoretical thing that's mainly good for arguing about. It's probably useful to get his students' brains doing something other than idling in neutral, but otherwise I don't see the point.

Plus, I don't think what he did is really a proof, it's just an argument. Which is fine, but it's not exactly the same thing.

[TyCobb]

But we don't deal with numbers that repeat forever. We always round them off. There are rules about how many digits of precision are appropriate, given other the factors of an equation.

.333333 is not the same as 1/3. It's an approximation of 1/3.
.666666 is not the same as 2/3. It's an approximation of 2/3.
Whenever you terminate it at X digits, you use rounding rules.
The rounding rules say that the approximation of 2/3 doesn't end in a 6, it ends in a 7.
So, .333333 + .333333 is not .666666, it's .666667.
Are you gonna claim that 3 + 3 = 7 ? I bet not...

So this is a just a theoretical thing that's mainly good for arguing about. It's probably useful to get his students' brains doing something other than idling in neutral, but otherwise I don't see the point.

Plus, I don't think what he did is really a proof, it's just an argument. Which is fine, but it's not exactly the same thing.

I posted the actually proof. My guess is his students won't be able to understand the real proof, so he gave the 1/3 + 2/3 = 3/3 example which isn't a proof at all.

[square634]

.9999999.... (repeating) is equal to 1. And here's the proof. (http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html)

.9 repeating equals one. In other words, .9999999... is the same number as 1. They're 2 different ways of writing the same number. Kind of like 1.5, 1 1/2, 3/2, and 99/66. All the same...

1/3=.33333333...
2/3=.66666666...
3/3=.99999999...

And 3/3=1, so .99999999....=1, too.

This kind of stuff makes my brain hurt.

Yay! Math!

I mean, that's not really a proof, but more of an intuition. The actual proof has more to do with infinite sequences and series. If this makes your brain hurt, you would not want to be a computer science major. For example, your intuition would be that there are twice as many integers as even integers. But we proved in our intro discrete math class using a bijection that the size of the set of even integers is the same as the size of the set of all integers. Russell's Paradox is also not much fun.

[The Epic]

But we don't deal with numbers that repeat forever. We always round them off. There are rules about how many digits of precision are appropriate, given other the factors of an equation.

.333333 is not the same as 1/3. It's an approximation of 1/3.
.666666 is not the same as 2/3. It's an approximation of 2/3.
Whenever you terminate it at X digits, you use rounding rules.
The rounding rules say that the approximation of 2/3 doesn't end in a 6, it ends in a 7.
So, .333333 + .333333 is not .666666, it's .666667.
Are you gonna claim that 3 + 3 = 7 ? I bet not...


Pretty much this. You can't just round and say that something equals something else, even if it goes infinite. As infinitesimal as the difference is, there is still a difference.

[Sanfran327]

It's not hard to understand:

1/3= .333333 repeating
2/3= .666666 repeating

1/3 + 2/3 = 1, so .3333 repeating + .6666 repeating should equal 1.

Actually, it's because the .3333333333 and the .66666666666 are not complete numbers. They go on for infinity.

And I may just be an Engrish Mager, but last I checked, 3+6=9, not 10.

[Sanfran327]

Pretty much this. You can't just round and say that something equals something else, even if it goes infinite. As infinitesimal as the difference is, there is still a difference.

Exactly. There is a difference. One third plus one third plus one third is one.

Almost one third plus almost one third plus almost one third is almost one.

It is not one.

I hate to break it to the OP, but .3333333 does NOT equal 1/3 no matter how much you want it to.

[The Wedge]

Actually, it's because the .3333333333 and the .66666666666 are not complete numbers. They go on for infinity.

And I may just be an Engrish Mager, but last I checked, 3+6=9, not 10.

I have an Engrish degree, and I can tell you, that even with my hatred and distrust of math that .3333...+.6666....=.9999... is not the same as 3+6=9.


I hate to break it to the OP, but .3333333 does NOT equal 1/3 no matter how much you want it to.

That's because it's not .3333333. It's .3333..., the repeating makes the difference.

And it's reasons like that which are exactly the reasons why I don't trust math. Universal language my left butt cheek.

[NewMarketSean]

Imagine the biggest number you can think of. Now add a 1 to it.

Brainsplode.

[Frobby]

Can't believe I'm doing this, but here's how I learned it:

x = .99999999......
10 x = 9.9999999.......
(10 x - x) = (9.99999999....) - (.999999....)
9x = 9
x = 1
Therfore, if x = .999999..... AND x = 1, then .999999....= 1.

Q.E.D.

[The Wedge]

Can't believe I'm doing this, but here's how I learned it:

x = .99999999......
10 x = 9.9999999.......
(10 x - x) = (9.99999999....) - (.999999....)
9x = 9
x = 1
Therfore, if x = .999999..... AND x = 1, then .999999....= 1.

Q.E.D.

That's pretty much one of the examples the link in the OP has.

Plus, Q.E.D., FTW.

[square634]

Pretty much this. You can't just round and say that something equals something else, even if it goes infinite. As infinitesimal as the difference is, there is still a difference.

It's really a definition thing. The reason that .33333333333... is the same as 1/3 is that the definition of 1/3 is actually 3/10 + 3/10^2 + ... + 3/10^n, as n goes to infinity. Even though infinity isn't directly tangible, denying the infinite in mathematics would undermine the foundation of many vital mathematical principles.

[Sanfran327]

Can't believe I'm doing this, but here's how I learned it:

x = .99999999......
10 x = 9.9999999.......
(10 x - x) = (9.99999999....) - (.999999....)
9x = 9
x = 1
Therfore, if x = .999999..... AND x = 1, then .999999....= 1.

Q.E.D.

If 'x' can have two DIFFERENT values in the same equation, then that's fiddle stix.

[The Wedge]

If 'x' can have two DIFFERENT values in the same equation, then that's fiddle stix.

...it doesn't have two different values, it proves that they are the same value. Which is the whole point.

How come the guy who absolutely hates math (me) is getting this? Is it because I'm much better with the ideas than the practical (which is why I was the only person who really "got" relativity in my college physics class, though I couldn't explain it to you if I tried anymore)?

[square634]

If 'x' can have two DIFFERENT values in the same equation, then that's fiddle stix.

That's the whole point. The equation holds, but obviously X can't have two different values, so those two numerical representations must be equal. It's sort of like proof by contradiction.

[TyCobb]

He is wrong. It is a mathematical proof and a pretty easy one at that.

http://upload.wikimedia.org/math/5/6/9/56949181a290ce561f27bd550a720392.png

Does everyone have me on ignore?

[The Epic]

Can't believe I'm doing this, but here's how I learned it:

x = .99999999......
10 x = 9.9999999.......

x is .9999 to the infinite, but 10x would lead to the last decimal place (even to the infinite) being 0.

So 10x-x = 9x = 8.99999999..............1

[square634]

x is .9999 to the infinite, but 10x would lead to the last decimal place (even to the infinite) being 0.

So 10x-x = 9x = 8.99999999..............1

There is no such concept as the "last" decimal place of an infinite decimal.

[TyCobb]

x is .9999 to the infinite, but 10x would lead to the last decimal place (even to the infinite) being 0.

So 10x-x = 9x = 8.99999999..............1

This is so wrong.

[Sanfran327]

That's the whole point. The equation holds, but obviously X can't have two different values, so those two numerical representations must be equal. It's sort of like proof by contradiction.


Does everyone have me on ignore?

The other day, I came thiiiiiiiis close to stepping in a huge pile of dog crap.

Sure am glad I missed it by a smidge.

[The Wedge]

I think the problem is that everyone puts math up as such a "concrete" science that when something like this pops up, something that you need to accept as infinite AND finite at the same time because, let's face it, it's what happens in this case, people sort of hold fast to the "known."

For the purposes of this equation, you really have to think to yourself "there is no spoon." Oh, wait, excuse me "the numbers are both infinite, and finite."

[The Epic]

YOUR FACE IS SO WRONG.

I kid. No, really, I know that was a horrible example, and I noted that to myself after I did it. :P

[The Wedge]

The other day, I came thiiiiiiiis close to stepping in a huge pile of dog crap.

Sure am glad I missed it by a smidge.

There is no smidge in this equation. The only smidge is in how you perceive .9999...

[Sanfran327]

There is no smidge in this equation. The only smidge is in how you perceive .9999...

The smidge is the difference between .33333... and a true 1/3.

[square634]

The other day, I came thiiiiiiiis close to stepping in a huge pile of dog crap.

Sure am glad I missed it by a smidge.

What's funny to me, having had the chance to study some upper-level math, is that there are actually parts of math in which there is still legitimate controversy, whereas this is an elementary definition that is taught at the middle school level. I never realized this was even a question. There are some things in math that you can't see in real life. Infinity is one of them. It is still a concept is necessary and is applied in ways that are used to improve people's live. Decimals and fractions are just two different ways of writing the same thing.

[TyCobb]

YOUR FACE IS SO WRONG.

I kid. No, really, I know that was a horrible example, and I noted that to myself after I did it. :P

There is no example you or anybody can find that will discredit the actually proof.

[Mackus]

There is no example can find that will discredit the actually proof.Hehe, you're not an English major :)

Your math is right though.

[DuffMan]

Is there really an argument going on about this? Usually these kinds of threads pop up in the middle of winter when there is hardly any O's news at all, but now?

[The Wedge]

The smidge is the difference between .33333... and a true 1/3.

Then like I said, until you're willing to acknowledge that the ...indicates "infinity" yet there HAS to be a finite number somewhere, you're always going to say "WRONG!" Because you have to acknowledge that before you can equate .3333... and 1/3. Otherwise you're saying that 1/3 has no equatable decimal, which would probably infuriate any number of math teachers/professors. ;)

[The Epic]

There is no smidge in this equation. The only smidge is in how you perceive .9999...

I agree with you saying that it's all about perception. There's not going to be an agreement here, I'm sure, but like I said, I feel that that there is a smidge.

[The Wedge]

What's funny to me, having had the chance to study some upper-level math, is that there are actually parts of math in which there is still legitimate controversy, whereas this is an elementary definition that is taught at the middle school level. I never realized this was even a question. There are some things in math that you can't see in real life. Infinity is one of them. It is still a concept is necessary and is applied in ways that are used to improve people's live. Decimals and fractions are just two different ways of writing the same thing.

I really think it's only a question because our numeral system has created this counter-intuitive phenomenon.

[TyCobb]

Hehe, you're not an English major :)

Your math is right though.

Negative, haha. Math minor when I was in college, but I swear someday I am going to force myself to learn how to write English properly.

[TyCobb]

I agree with you saying that it's all about perception. There's not going to be an agreement here, I'm sure, but like I said, I feel that that there is a smidge.

There is no smidge from .333... and 1/3 it is the same number just like how
.999... = 3/3 = 1

It isn't an approximation, it is a mathematical proof which was solved back in the 1700s.

[Sanfran327]

I was watching the animal planet, did you know that the male seahorse has the baby? Why don’t they just call that one the female? It's like some stubbron scientist said one day, "Yeah, this one here's the male seahorse."

And some other guy says, "Uhh, Bob... That one's having a baby."

"Yeah, the male has the baby."

[The Epic]

There is no smidge from .333... and 1/3 it is the same number just like how
.999... = 3/3 = 1.

Sure, and that's fine.

[waroriole]

There is no smidge from .333... and 1/3 it is the same number just like how
.999... = 3/3 = 1

It isn't an approximation, it is a mathematical proof which was solved back in the 1700s.

Man, for the longest time I thought you were disagreeing with the me and the OP. I worked through your equation and decided you either didn't know what you were talking about or I was missing something. Glad to see we're both right.:D

[Lefty0315]

I am glad I gave on math when they started taking away 2 of my 3 apples is first grade.

[McLovin]

I was watching the animal planet, did you know that the male seahorse has the baby? Why don’t they just call that one the female? It's like some stubbron scientist said one day, "Yeah, this one here's the male seahorse."

And some other guy says, "Uhh, Bob... That one's having a baby."

"Yeah, the male has the baby."
I read this 6 times, and laughed each time. Theoretical rep vibes to you.

[Nigel Tufnel]

I am glad I gave on math when they started taking away 2 of my 3 apples is first grade.

When did you give up on English?:D

[Sanfran327]

I read this 6 times, and laughed each time. Theoretical rep vibes to you.

Gaffigan = funny.

I can dig that equation.

[scOtt]

The main disconnect is in the fact that it's .9 *repeating*. In essence, that *repeating* means infinity, but it also has to be a finite fixed number...it's a paradoxical problem that ends up making in another paradox of .99999... = 1.

I still don't trust math.
It's been a while, but I've seen this proven, not surmised.

It's true. ;)

[Flip217]

I have a hard time buying this. If you take a small portion of any object away, you no longer have the whole object.

You have almost a whole object.


Pretty much this. You can't just round and say that something equals something else, even if it goes infinite. As infinitesimal as the difference is, there is still a difference.

I think this response from the site I linked to addresses your posts:

".9 repeating is obviously less than 1."
Hmmmm...it might be obvious to you, but it's not obvious to me. Is it really less than 1? How much less than 1? No, seriously...tell me how much less? What is 1 minus .99999999...?

[The Epic]

I think this response from the site I linked to addresses your posts:

".9 repeating is obviously less than 1."
Hmmmm...it might be obvious to you, but it's not obvious to me. Is it really less than 1? How much less than 1? No, seriously...tell me how much less? What is 1 minus .99999999...?

I get this, but TyCobb's equation from several posts ago makes more sense than anything else, to be honest. There's no reason to discuss it further.

But to humor you, it's .000000000......

[Flip217]

Another explanation from the site that I didn't really get at first, but makes sense now...

"The definition of the sum of an infinite geometric series (and other series, too, but we won't get into those) goes something this:

* Start making a list of partial sums: the sum of the first one number, then
the sum of the first two numbers, then the sum of the first three, etc.

* Examine your list closely. In this case the list is: .9, .99, .999, .9999, .... (Note that the actual number .99999.... is not on the list, since every number on the list has finitely many 9s.)

* Find some numbers that are bigger than every single number on your list. Like 53, 3.14, and a million.

* Of all the numbers that are bigger than every number on your list, find the smallest possible such number. I think we can all agree that this smallest number is 1.

* That smallest number that can't be exceeded by anything on the list is the definition of the sum of the geometric series.

Notice that I keep putting the word definition in bold face. (See, I did it again!) That's because it's a definition, which isn't really up for debate. It is the nature of a mathematical definition that once you acccept it, you have to agree to its consequences. In other words, .99999... = 1 by the definition of the sum of a geometric series"

[BRobinsonfan]

If 1 = .999... the what does 2 =?

[TGO]

Camelot is a silly place.

[BaltimoreTerp]

If 1 = .999... the what does 2 =?

http://images3.wikia.nocookie.net/uncyclopedia/images/b/ba/Scanners.gif

[Austin]

But to humor you, it's .000000000......

Oh, so you mean 0?

[The Epic]

Oh, so you mean 0?

No. 0.000000000....... ;)

[TyCobb]

if 1 = .999... The what does 2 =?

1.999.....

[Satyr3206]

I am theoretically eating a Pit Beef sandwich right now. Quantum consumption.

[weams]

It all started when a time travel experiment I was conducting went... a little ka-ka. In the blink of a cosmic clock I went from quantum physicist to air force test pilot. Which could have been fun... if I knew how to fly. Fortunately, I had help. An observer from the project named Al. Unfortunately, Al's a hologram, so all he can lend is moral support. Anyway, here I am. Bouncing around in time, putting things right which once went wrong. A sort of time traveling Lone Ranger, with Al as my Tonto. And I don't even need a mask.


Oh boy.

[weams]

In other words "I told you this was going to be a ride!" (http://forum.orioleshangout.com/forums/showthread.php?t=49428)

[BRobinsonfan]

1.999.....

OK smart guy. What does 1.999... = ? :)

[TyCobb]

ok smart guy. What does 1.999... = ? :)

1.999... = 2 = 2/1 = 4/2 = 6/3

[Coker]

http://i173.photobucket.com/albums/w72/armandop27/HangmanMath.gif