What is .99 repeating as a fraction?
Quote: weaselmanNo, it wasn't. He just misspoke about rounding, that's all.
You "agree" with what? That 1.0 is not equal to 1?
I guess, that's the end of the discussion then. I must admit that you have a very original and unorthodox view of elementary math.
That's not what I meant. I was not talking about your species recognition skills at all.
What did I say about speaking from the top of your head?
Did you and Triplell have a discussion I don't know about? Or, are you just making up some B.S.? I know, you misspoke, you're certainly not trying to B.S. me and say you know what triplell meant by 1.000... can be rounded down to 1. Are you? Maybe, you should ask him.
1.0 is equal to 1. At least I think so. Problem is does 1.000... = 1. I'm saying they're completely different numbers. :)
That's not what I meant. I was not talking about your species recognition skills at all.
You misspoke then.
Quote: TriplellSorry, I meant 1.000... is rounded down to 1. You do realize that 1.000... = 1, don't you? If you didn't realize, I'm making a mockery of you. Technically, all numbers could be represented as repeating decimals. 1 = 1.000..., 2 = 2.000..., (3/2) = 1.5000...
Get my point.
You don't "round" .999... to 1, because it is 1. Same way, you don't round 1.000... to 1, because it is 1.
PS: Maybe you should straighten me out yourself.
See, first off, I'm not a BSer.
You on the other hand seem to be a troll. You quoted only the top portion of the above quote. You completely skipped over the point I made that all numbers can be represented as a repeating decimal, however no one represents it like that, as it is just extra work to represent the same number.
I never misspoke about rounding. I may have misspoke about calling 667/1000 "close" to 666/999, as close depends on the context of the situation.
Back to rounding, you incorrectly introduced the fact that .999... rounds to 1. The number doesn't "round" to one, because it is one. This won't get through your head, however, because you are on this forum to argue.
At one point in my life, I would have agreed with you that .999... repeating doesn't equal 1, but then I learned math...
You should look into learning math as well.
Quote: TriplellSorry, I meant 1.000... is rounded down to 1.
Talk it over with MathE, kid. It's either equal to 1 or it's not. You picked both.
Instead of arguing about rounding though (which is not what this thread is about, until you introduced it (incorrectly I might add))
How about you give me a proof to where 1.000... != 1 or 0.999... != 1?
PS: You shouldn't quote people out of context, JyBrd.
Quote: Triplell
I never misspoke about rounding. I may have misspoke about calling 667/1000 "close" to 666/999, as close depends on the context of the situation.
Back to rounding, you incorrectly introduced the fact that .999... rounds to 1. The number doesn't "round" to one, because it is one..
Hey, kid, round .999... off for me and tell me what you get? I incorrectly did what? I thought MathE was a bad B.S.er you're taking the cake, kid. Somebody told me not to waste time with you guys. I thought maybe I could help. You had better get a lot better at your B.S. kid. Because, right now you're making a jackass out of yourself.
.999... = 1 . What on your word. You make too many mistakes to take your word on the subject, kid. But, the biggest point is your Full of Sh**. You, better say that some really smart guy a thousand years ago wrote a book and proved it was so. And, you better hope that guy wasn't Full of Sh**.
Hey, kid, round .666... off for me and tell me what you get? I get .6666667. My friend got .667. Same number right, kid?
Drunk and upset today.
Too bad they are choosing this forum though...
Quote: WongBoGlad to see they are letting psych patients use the computer.
Too bad they are choosing this forum though...
I agree, WongBo.
His depression is probably caused by gambling, which is why he is on this forum. He doesn't understand that the casino will take his money, which piles onto his depression, and thus he drinks more.
It's ok. You obviously are just down on your luck. The world didn't give you as many opportunities as it gave the rest of us....
Quote: JyBrd0403I thought MathE was a bad B.S.er you're taking the cake, kid.
But, the biggest point is your Full of Sh**.
Drunk and upset today.
Personal insult -- 7 day suspension.
By the the way, being drunk and upset or using asterisks are not an excuse.
Yep, I think the Wizard's adjusted policy on free speech could be applied to the trolling and attitude problems in this thread. In case you haven't read it:Quote: JyBrd0403Drunk and upset today.
Quote: Wizard (in another thread)Let it be known that I feel my liberal free speech policy has been abused lately and I'm going to be restricting that some more, in favor of the greater good of the forum.
Edit: Whooops! Slow typing combined with an accurate prediction!
Quote: JyBrd0403What did I say about speaking from the top of your head?
I have no idea. I never pay much attention to senseless ramblings, sorry/.
Quote:Did you and Triplell have a discussion I don't know about?
No idea what you know either, sorry.
Quote:
1.0 is equal to 1. At least I think so. Problem is does 1.000... = 1.
I'm saying they're completely different numbers. :)
Different numbers? What's the difference between them? I mean, what's the value of the difference?
Quote:You misspoke then.
Nope. I did not.
Quote: weaselmanNope. I did not.
Very well. Someone had said on a different thread KBO. I didn't know exactly what it meant, but it did ring a bell for me. Then, someone said KBO means Keep the Bastards Out.
You see, I don't use that term. I recognized the term KBO, but I couldn't put the meaning together.
You keep telling me you misspoke and you don't understand, child's play. I don't understand why 2+2 doesn't equal 7. I misspoke... I don't understand... You could do this forever...
You see, the problem is, I'm a tough guy, sooner or later, you have to face facts. That I misspoke ... I don't understand... stuff ain't going to work for you. So, KTA. KBO what's the point, KTA.
KTA - Kill Them All!
- KTA All the Way -
Quote: MichaelBluejayWhat gets me about this discussion is how some people, with minimal training, are confident enough to insist that they're right and all the world's experts are wrong. That just seems a little...arrogant.
Even people with training disagree with this, although it is a minority. You guys just won't accept the different viewpoint and what it is attempting to explain. I said this many pages ago, and I'm not getting back into the question, but there are mathematicians that disagree with the .999... = 1 majority. Not just lay people and neanderthals with "minimal training."
It isn't confidence btw, it is just a different way of thinking. I even submitted, FROM the beginning, that both competing sides have valid points and that I didn't expect a single person to accept anything, AND that my point of even participating in this thread, was to explain the rationale, and not to CONVERT anyone.
Arrogance? Hardly. (Of course I'm only speaking for myself.)
Quote: JyBrd0403V
You keep telling me you misspoke and you don't understand, child's play.
Me? You told me that I misspoke. And I never told you you did not understand either.
I don't think you don't understand actually. Frankly, there isn't much to be understood here.
Quote:You see, the problem is, I'm a tough guy,
Tough? No ... Just stubborn. It's not the same thing.
Quote: YoDiceRoll11Even people with training disagree with this, although it is a minority.
Maybe ... if you are talking about medical training ... or VAC, perhaps. Not math training.
Quote:You guys just won't accept the different viewpoint and what it is attempting to explain.
We are talking about an axiomatic theory here. There are no viewpoints. Each statement is exactly either true or false. (And don't bring Goedel into this. Yes, I know about his theorem, and no, it does not apply here).
Quote:I said this many pages ago, and I'm not getting back into the question, but there are mathematicians that disagree with the .999... = 1 majority.
No. There aren't. Or they are not mathematicians (if you saw someone on internet saying this, and claiming that he is a mathematician, then he is lying. I mean, maybe he managed to get his diploma somehow, but he certainly does not know what he is talking about. Or else, you simply misunderstood what he is saying, like with all those "alternate theories"). I don't remember you saying it before (you did say something about "alternative theories", and I explained then why it was wrong), but, if you did, you were wrong.
Quote: weaselmanMe? Tough? No ... Just stubborn. It's not the same thing.
No, I mean tough guy.
Quote: JyBrd0403
No, I mean tough guy.
I know what you mean. I said, that you do not come across as a tough guy. More like a stubborn chick. And also, not entirely honest if your frivolous treatment of qoutations is any indication.
Quote: YoDiceRoll11Even people with training disagree with this, although it is a minority.
Really? Name one.
Quote: weaselmanWe are talking about an axiomatic theory here. There are no viewpoints. Each statement is exactly either true or false.
People are getting hung up on trying to wrap their minds around infinite/infinitesimal. The difference between .9999.... and 1 is an artifact of the way numbers are notated, not a difference in their actual value.
Yes, I agree that it is about the notation.Quote: MoscaPeople are getting hung up on trying to wrap their minds around infinite/infinitesimal. The difference between .9999.... and 1 is an artifact of the way numbers are notated, not a difference in their actual value.
0.090909... + 0.909090...Quote: ALFERALFER1/11 + 10/11
___________
1
.99999..........
Quote: weaselmanI know what you mean. I said, that you do not come across as a tough guy. More like a stubborn chick. And also, not entirely honest if your frivolous treatment of qoutations is any indication.
Stubborn Chick? Haven't been called that one before. I have been told that I fight like a chick, though. That should give you some confidence.
Watch what I do to your math in a couple of posts.
Quote: MichaelBluejayQuote: YoDiceRoll11Even people with training disagree with this, although it is a minority.
Really? Name one.
William timothy Gowers, Robert Ely, Ian Stewart, Jose Benardete, Karin Katz and Mikhail Katz, all are mathematicians that argue that .999... doesn't equal zero. That's just from the wikipedia link the Wiz posted a while back in this thread. I'm sure I could find plenty more if I cared to delve into it.
That should be they argue .999... doesn't equal one.
x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x=1
If I'm not mistaking, this is the equation where whatever number you put in the top of the equation is the same number you get at the bottom of the equation. Drop the number 8 into the top of the equation, and you get 8 on the bottom, right? See, they didn't prove .999... is eqaual to 1, they proved that this equation doesn't work for all numbers.
You wanted a mathematical proof .999... is not equal to 1, here it is.
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
x = .999...
With this equation any number you put into the top of the equation, you will get the same number on the bottom. Put 8 into the top of the equation, and you will get 8 on the bottom. And, guess what:) put .999... into the top of the equation, and you get .999... at the bottom. That's proof .999... = .999... and not 1.
Personally, if you give me .999... and ask me to do an equation with it, I'm just going to round it off to 1 anyway, and then do the equation. If you tell me the answer is 3.999... and my answer is 4, I might say something smart ass, like what's the difference? However, I won't say 4 is equal to 3.999..., I might lose my mind, along with my head, doing something like that. ROTFL.
Quote: JyBrd0403
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
x = .999...
So what number do you add to 9.999... to get 10.999...? Looks to me like you are adding 1..or is it .999...
So to answer your question I'm adding .999... and not 1 to this equation.
I guess, that should be 9.999 + .999 = 10.998, then 9.99999 + .99999 = 10.99998, .999... goes on for infinity, therefore 9.999... + .999... would equal 10.999...
What can I say, drunk again tonight.
The answer to your question is still, I'm adding .999.. and not 1 to this equation.
Do the math. Tell me I'm wrong.
Just trying to make sure you know what I'm saying here. That's why I'm saying do the math for yourself.
Watch this.
That proof I gave out in the previous post. It's just BS.
They're gone.
Don't worry about it.
Like I'm talking to myself here. LOL.
Wasted tonight. LOL.
Not what I imagined it to be, while I was on suspension for 7 days. Give a proof like that, and there's no response(triplell not included). Weak. I dreamed up an immediate apology. Wishful thinking I assume. Oh well, temporary problem, life is. Tough guy, toughest. LOL.
You've got the proof, do the math for yourselves.
How's that proof working out. :)
Quote: GamerManexcept you only proved with your "proof .999999... doesn't equal 1" that .99999999999... = .999999999999..., which does not disprove .9999999 = 1 at all. It would be like me saying 1 + 1 != 2 because 1 + 1 = 1 + 1
Seriously? Maybe, you missed it. With this equation, any number you put into the top of the equation, will be the SAME number that comes out on the bottom of the equation. If .999.. actually equaled 1, you would put .999... into the top of my equation, and it would come out as 1 at the bottom of this equation, at least 50% of the time, since you're saying .999... equals 1 or .999... Either that, or, my equation is BS.
In reality, you put .999... into the top of my equation and it will come out as .999... every single time. What do you think of my equation? Do the math for yourself.
Use that ! symbol again with me. I did some research, I know what that symbol means now. I got a question for you. If I round .999... off does it equal .999! By the way, 1 + 1 = 2. 1 + 1! = 2, also.
Alright 1 + 1! = ? to me right now.l Took me a second, but then again, I think you understand what the symbol ! means. 1 is a whole number, I don't think you can put a ! behind it. Maybe I need to do some more research, but, I'll say it again, use that symbol again with me.
No, I take it back, 1 + 1! = 2. Don't use that ! anymore, it's a BS point.
Okay, if you put .999... into the top of my equation, and it came out as 1 on the bottom of the equation, it would mean my equation was BS.
So, put .999.. into the top of the equation. See what happens.
What do you think, Mustangsally? I think the proof is pretty good. Matter of fact, now I'm positive it's good. :)
Quote: JyBrd0403Stubborn Chick? Haven't been called that one before. I have been told that I fight like a chick, though. That should give you some confidence.
That's the same thing. Argument is a lot like a fight.
Quote: JyBrd0403
William timothy Gowers, Robert Ely, Ian Stewart, Jose Benardete, Karin Katz and Mikhail Katz, all are mathematicians that argue that .999... doesn't equal zero. That's just from the wikipedia link the Wiz posted a while back in this thread.
No, you are confused. They are all talking about the "non-standard analysis" interpretation, not traditional calculus. This has been discussed before here.
If what you mean by 0.999... is a hyperreal number 0.999...;999000..., then it is indeed not equal to 1, just infinitely close to to.
But, this is just a terminological confusion. First, it is more logical to assume that 0.999... represents 0.999...;999...,
which actually is still equal to 1, and, more importantly, this thread is about real numbers.
There is no dispute among mathematicians (or anyone else with any sufficient knowledge of math) that a real number 0.999... is an alternative representation of 1.
While there is indeed some ambiguity in the non-standard analysis, note that the root of that is not the lack of agreement about the nature of the real number ("1"), but rather the deficiency in the notation representing infinitesimals, and mapping hyperreal numbers to real. This is entirely orthogonal to the discussion.
Quote: JyBrd0403Here's a proof From Wikipedia that .999... is equal 1...
x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x=1
If I'm not mistaking, this is the equation where whatever number you put in the top of the equation is the same number you get at the bottom of the equation.
Yeah, you are mistaken. You don't "drop" anything there. The value of x is defined in the first line. Then some arithmetic operations are performed on it, and the last line shows the same value (x) in a different notation. If 1 is not the same thing as 0.999... then one of the operations between the first and last lines must be invalid. Since that is not the case, that means that x equals to 0.999... and to 1 at the same time. Therefore 0.999... = 1
Quote:
You wanted a mathematical proof .999... is not equal to 1, here it is.
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
x = .999...
No, this is not it. It proves that 0.999... equals to 0.999..., which is true. But it does not disprove that it also equals to 1. In fact, it actually uses this fact between lines 3 and 4, where adding .999... to 9 turns it ... into a 10 :)
Quote: JyBrd0403With this equation, any number you put into the top of the equation, will be the SAME number that comes out on the bottom of the equation.
Exactly! 0.999... is the same number as 1. That's why it "comes out on the bottom". You got it!
Quote: weaselmanThat's the same thing. Argument is a lot like a fight.
I don't think you get it. Wing Chung Kung Fu was developed by a woman.
Quote: JyBrd0403I don't think you get it. Wing Chung Kung Fu was developed by a woman.
Yes. Some women do not fight (or argue) like chicks. Some men do on the other hand.
You said yourself, you are going to round .999... to 1 anyway.
I can tell you that, you are not rounding, that .999... is 1, but it doesn't really matter, because in the end, our result is we end up with 1.
So i'm going to go ahead and let you "round" .999... to 1 all you want. If you acknowledge that adding .999... to 9.9999 = 10.999... then that is fine with me.
Quote: JyBrd0403
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
You assume here 9.999.... + 0.9999.... = 10 + 0.999.... this doesn't follow, unless 9.9999.... = 10.
Quote:
x = .999...
You assume 10.999.... / 11 = 0.999.... this doesn't follow either from the previous step.
Moreover, You need to prove 0.9999... != 1. All you prove here is 0.999... = 0.999....
No, I'm not assuming it equals 10 + .999... I'm adding 9.999... + .999...Quote: thecesspitYou assume here 9.999.... + 0.9999.... = 10 + 0.999.... this doesn't follow, unless 9.9999.... = 10.
You assume 10.999.... / 11 = 0.999.... this doesn't follow either from the previous step.
Moreover, You need to prove 0.9999... != 1. All you prove here is 0.999... = 0.999....
Grab a calculator. 9.999... + .999... = 10.999....
No, I'm not assuming. I'm just doing the math.
No, I don't need to prove .999...! = 1. You do.
Your guys proof doesn't work for all numbers, even though you say it does.
Quote: JyBrd0403No, I'm not assuming it equals 10 + .999... I'm adding 9.999... + .999...
Grab a calculator. 9.999... + .999... = 10.999....
Of course. Because 0.999... = 1, and 9+1=10.
Quote: TriplellIf you don't recognize a difference between .999... and 1, why argue that they are different?
You said yourself, you are going to round .999... to 1 anyway.
I can tell you that, you are not rounding, that .999... is 1, but it doesn't really matter, because in the end, our result is we end up with 1.
So i'm going to go ahead and let you "round" .999... to 1 all you want. If you acknowledge that adding .999... to 9.9999 = 10.999... then that is fine with me.
I agree with you. It's really semantics to me. But, at the same time, sometimes you want to know what is what. You know, you either rounded the number or you didn't. Hence, this thread, I assume. LOL
Quote: JyBrd0403I got a question, though. Does my proof work for all number, including .999...?
Your guys proof doesn't work for all numbers, even though you say it does.
Doesn't need to.
The hypothesis is 1 = 0.999....
The proof is given, and the last line of the proof shows 1 = 0.999....
Your proof does not show 0.9999.... != 1.
Thus it is not a proof.
Quote: JyBrd0403No, I'm not assuming it equals 10 + .999... I'm adding 9.999... + .999...
You proof clearly turns 9.999.... into 10 in one line.
Quote:
Grab a calculator. 9.999... + .999... = 10.999....
Which calculator model do you have that represents 9.999...?
Quote:
No, I don't need to prove .999...! = 1. You do.
No I don't. I have shown a proof that 0.9999... = 1. I cannot prove 0.999... != 1, because I don't make that hypothesis. It's assinine to state "X is true, now you go prove it, though you have stated X is false".
Express 0.99999... as 9 x 10-1 + 9 x 10-2 + 9 x 10-3 + ... + 9 x 10-N + ...
Let X = X1 x 10-1 + X2 x 10-2 + X3 x 10-3 + ... + Xn x 10-N + ...
with all Xn as integers >= 0
Let N be the smallest positive integer such that XN <> 9; if it is > 9, X >= 1, and if it is < 9, X < (1 - 10N + 10N+1).
Therefore, there are no real numbers > 0.99999... and < 1.
Let X = 0.9999999....., and assume X < 1
X < 1
Add X to both sides: X + X < X + 1
Add 1 to both sides of X < 1: X + 1 < 1 + 1
X + X < X + 1 < 1 + 1
2X < X + 1 < 2
X < (X + 1) / 2 < 1
Therefore there is at least one number greater than X and less than 1 - but that contradicts the original statement that no such number exists.
I think the main problem is, is the number of digits in 0.9999999... considered "countable"?
Quote: thecesspitYou proof clearly turns 9.999.... into 10 in one line.
No I don't. I have shown a proof that 0.9999... = 1. I cannot prove 0.999... != 1, because I don't make that hypothesis. It's assinine to state "X is true, now you go prove it, though you have stated X is false".
You add 9.999... + .999... and tell me what the answer is. Don't round .999... to 10 just add 9.999.... + .999... and tell me what you get.
Maybe it's me, .999...! you mind defining this for me. I really hate that ! symbol.
Quote: JyBrd0403
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
x = .999...
Just for fun, I put that .999...! thing you gave me, into the hopper. I dropped, .999...! into the top of the equation, and it came out .999...! on the bottom. I love this equation, it works much better then your guys equation.
Quote: JyBrd0403You add 9.999... + .999... and tell me what the answer is. Don't round .999... to 10 just add 9.999.... + .999... and tell me what you get.
Maybe it's me, .999...! you mind defining this for me. I really hate that ! symbol.
I don't think anyone is using the ! symbol, which usually means "factorial". Some posters here use the two-character symbol != for "not equal". I assume that is because they are not confident that the usual symbol of ≠ will show up properly for everyone. (Did it look right to you when I just used it?)
Edit: Slow post once again.
