Is 1 = 0.9999......

[RossGr]

Originally posted by: ndee
so 1.99999999999999999999999999999999999... = 2?

NdeeD

 

[AmbitV]

Originally posted by: RossGr

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.

Thx, edited to reflect that. What I said still stands.

 

[RossGr]

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.

Thx, edited to reflect that. What I said still stands.

ahh! another self taught mathematician, with no clue.

 

[spidey07]

LOL.

Still the same - folks who know the real number system realize and have proven that .9 = 1.

The folks who have some other magical doctrine of divine non-reality simply disagree.

Thanks again RossGR for actual proofs.

 

[MadRat]

Originally posted by: josphII

Originally posted by: MadRat
There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

yes there is, its called the principles of addition, subtraction, multiplication, and divistion - the basis for every mathematical function including every expression in the proof of 0.999... = 1

Used within their original context you can likely make them principles say it does not.

 

[AmbitV]

Originally posted by: RossGr

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.

Thx, edited to reflect that. What I said still stands.

ahh! another self taught mathematician, with no clue.

no clue? If you think ".999..." is exactly the same as "1", you are the one with no clue. I can already prove they're different in at least one way - it took more keystrokes to type one than the other.

 

[Muzzan]

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.

Thx, edited to reflect that. What I said still stands.

ahh! another self taught mathematician, with no clue.

no clue? If you think ".999..." is exactly the same as "1", you are the one with no clue. I can already prove they're different in at least one way - it took more keystrokes to type one than the other.

So 8/4 and 2 are not the same number, since it takes more keystrokes to type 8/4?

 

[AmbitV]

Originally posted by: Muzzan

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman

Originally posted by: RossGr

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.

Thx, edited to reflect that. What I said still stands.

ahh! another self taught mathematician, with no clue.

no clue? If you think ".999..." is exactly the same as "1", you are the one with no clue. I can already prove they're different in at least one way - it took more keystrokes to type one than the other.

So 8/4 != 2, since it takes more keystrokes to type?

8/4 = 2

I'm only pointing out that there IS some difference between "8/4" and "2". Mathematically, they may be equilvent. Ulitmately, however, we have to convey all our idea, including mathematical concepts, using language. And there is some difference between the two symbols. In the same way "current president of the united states" and "husband of laura bush" might be the same person, but obviously there is some difference between the two phrases. Frege thought that the difference lies in "sense" - the two phrases have the same denotation, but not the same sense. What sense amounts to is a complicated topic.

Now the question I want to raise is, are symbols like "8/4" and "2" at a higher level of abstraction, like "husband of laura bush"? Do they have referents, in the same way "husband of laura bush" refers to the person George Bush? If so, what do numbers refer to? Are numbers concepts?

 

[RossGr]

It seems clear that those who have no knowledge of mathematics beyond arithmetic believe that it is a trivial topic with no sublity or depth. Arithimetic is pretty much what you see is what you get, but math is much much more then simple arithemictic. If all you know is that tiny fragment of the whole then you should open your eyes to a larger world.

 

[Turkish]

gotta love math gurus fight I hate math

 

[Hector13]

Originally posted by: MadRat

Originally posted by: josphII
yes there is, its called the principles of addition, subtraction, multiplication, and divistion - the basis for every mathematical function including every expression in the proof of 0.999... = 1

Used within their original context you can likely make them principles say it does not.

if you think you can, then do so. Don't say its "likely". Either you know how to show that .999... != 1, or you don't know what you are talking about.

All these people have posted proofs of why they are equal, and you haven't posted any concrete evidence to the contrary (no, what you "believe" is not evidence). You point of view should be simple to prove. You claim .9999r != 1, so:

.999... < x < 1
or:
1 - .999... = y

All you have to do to prove you are right is tell us what x or y is. What could be simpler?

 

[ElFenix]

Originally posted by: MadRat
There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

if you can't argue within the system you're doing nothing more than trolling.

 

There is no 1.

 

[DrPizza]

Originally posted by: MadRat

Originally posted by: cheapbidder01
Anyone who argues otherwise never got an A above basic Algebra. If they did, then their teacher was wrong or too lazy to give them a proper grade.

Another assumption that is plain wrong. Just because a person doesn't become a math major doesn't mean squat about their comprehension of math. Interesting that you'd introduce the idea of "grades" as being proper one way or another. Reminds me of the debate about percentiles for grades as opposed to pass/fail. I've seen plenty of students with grade point averages above 100%, from deans nonetheless, so does that make professors that refuse higher scores that 100% any less elite?

If someone who hasn't majored in math who thinks they know a lot of math, they have absolutely no clue that they understand less than 1% of the field of mathematics. I majored in math... I had a 4.0 in mathematics.... I've taken additional math courses for 3 1/2 more years... I read mathematics journals occasionally...
And, one thing that I've learned through all the math that I've learned is that NO ONE will ever be an expert in all of mathematics ever again. The field is too broad now. It'd be like finding a doctor who is a brain specialist, and a heart specialist, and a bone specialist, and a kidney specialist, and.... (name all the specialists). Then, multiply that by 10. What you seem to refer to as "comprehension of math" may be more of what your intuition tells you.... and, intuition can be wrong. (especially if someone's intuition tells them that .999.... doesn't equal 1)

 

Can't you prove anything with a large enough dataset?

 

[DrPizza]

Nope. Although, there have been some proofs that have been proved by exhaustion (checking every possibility). But, proof by exhaustion doesn't work with an infinite set of possibilities, unless those possibilities can be grouped into a finite number of cases.

 

[spidey07]

I'd like to point out that the math gurus are not fighting. They are agreeing.

 

[XZeroII]

Infinity is NOT a number. It is an abstract concept that has no number assigned to it. Thus, there is no number that you can subtract from 1 that will equal .99999r (zero is not a number). You can say that that answer is 1/infinity (1-1/infinity=.9999r) but since infinity is not a number, you can't divide infinity into 1. Even if you think about it logically, how many times does infinity fit into one? Zero times. If you have an infinate amount of wood, and you want to put that wood into a shed, how much of that wood could you put into the shed (as a relation to what you started with)? None! You would put 1 into the shed, but you would still have an infinate amount of wood! The amount of wood you have has not changed, thus you actually didn't put any wood into the shed, because you have the same amount you had when you started. So 1/infinity = 0. 1-1/infinity = 1.

 

[ElFenix]

Originally posted by: XZeroII
Infinity is NOT a number. It is an abstract concept that has no number assigned to it. Thus, there is no number that you can subtract from 1 that will equal .99999r (zero is not a number). You can say that that answer is 1/infinity (1-1/infinity=.9999r) but since infinity is not a number, you can't divide infinity into 1. Even if you think about it logically, how many times does infinity fit into one? Zero times. If you have an infinate amount of wood, and you want to put that wood into a shed, how much of that wood could you put into the shed (as a relation to what you started with)? None! You would put 1 into the shed, but you would still have an infinate amount of wood! The amount of wood you have has not changed, thus you actually didn't put any wood into the shed, because you have the same amount you had when you started. So 1/infinity = 0. 1-1/infinity = 1.

 

[MadRat]

Originally posted by: XZeroII
So 1/infinity = 0. 1-1/infinity = 1.

Your proof missed your own point. If you solve for 1 then you'd get ( (1/infinity) * infinity) = (0 * infinity), so that 1=0.

Maybe you meant to say something else. If you want to get generalized then you could argue that null, one (its all inclusive form), and infinity are all abstracts.

 

[josphII]

Originally posted by: MadRat

Originally posted by: XZeroII
So 1/infinity = 0. 1-1/infinity = 1.

Your proof missed your own point. If you solve for 1 then you'd get ( (1/infinity) * infinity) = (0 * infinity), so that 1=0.

Maybe you meant to say something else. If you want to get generalized then you could argue that null, one (its all inclusive form), and infinity are all abstracts.

wrong again madrat. infinity/infinity != 1

 

[Syran]

It's been a while since I did the math for this... and I can't believe this thread is still alive.

Really, pretty much any time you play with infinate values, you deal with some form of limit.
As such, while .999... != 1, the limit is (iirc, been 5 years since i've done any of this)

Also, iirc:

infinity - infinity = any real number between -infinity & +infinity, since one infinity can be larger then the other, using this same rule, infinity / infinity is any real number greater then 0.

Hense, as .999... approaches the infinate number of repeating 9's, it gets closer and closer to 1, but never actually reaches it.

also, any defined number / infinity = 0 in sort of the same respect, since infinity can't be actually defined, it must be larger then the defined number, thereby being reduced to 0.

Now, 1 / 0 is just lunacy, can't happen, very undefined... since you aren't splitting anything, then it just gets thrown out. However, with inifinty being the divisor, it's just a number being split an infinate number of ways, so it gets reduced down to nothing.


I ever mention I hated limits?

 

[Muzzan]

How can a number have a limit...? How can a number approach another number ("2,95 aproaches 3"?)? Also, in 0,9r aren't the infinite number of 9's already there from the beginning?

 

[Jeff7181]

I'm no rocket scientist, but how to do you get 9x=9 from 10x - x = 9.9999... - 0.9999... ??????

Also... you're assuming right off the bat that x=.999... if that's true, then your conclusion is false, because that formula proves that x-.999... not that 1 = .999...

By that reasoning, I can prove that 5=1 too...

5=x
thus 5x = 6x-x
(5x)/x = ((6x)-x)/x
5=6-x
5=1

 

[Muzzan]

I'm no rocket scientist, but how to do you get 9x=9 from 10x - x = 9.9999... - 0.9999... ??????

Subtraction.

Also Jeff, I'm afraid you forgot to divide ALL terms by x in your "proof"!

x = 5
5x = 6x - x
(5x) / x = (6x - x) / x
5 = 6x/x - x/x
5 = 6 - 1
5 = 5

(Which is obviously true. )