View Full Version : 0,9999999=1

Markus

09-29-2008, 06:59 PM

just testing the new postcount feature, spam spam spam <3

Anyways, a friend of me said that 0,99999999 etc (9's in the infinity) = 1, because you can't do 1 - 0,0(infinite zeros here)1. Imo it isn't that way, because there is always a difference, what are your opinions?

ShowerThoughts

09-29-2008, 07:02 PM

0,9999999(infinite) = 0,9999999(infinite)

1 - 0,0000(infinite zeros ) = 1

sirlaughsalot

09-29-2008, 07:02 PM

What he is saying is 1/9=.111111 ect 2/9=.22222 ect until 8/9 which =.888888... so where is the .99999? This discussion was on sythe some time back...

Wizzup?

09-29-2008, 07:10 PM

just testing the new postcount feature, spam spam spam <3

Anyways, a friend of me said that 0,99999999 etc (9's in the infinity) = 1, because you can't do 1 - 0,0(infinite zeros here)1. Imo it isn't that way, because there is always a difference, what are your opinions?

EDIT: Hmm.

TViYH

09-29-2008, 07:29 PM

To get from 1 to .9999..., you can't just subtract .000...1, you'd go too far.

So in essence, they'd have to be the same thing.

More to find out: http://mathforum.org/library/drmath/view/55746.html

Torrent of Flame

09-29-2008, 07:33 PM

Wikipedia gives several proofs:

http://i34.tinypic.com/10eki1u.png

http://i34.tinypic.com/2ylqjqh.png

http://i36.tinypic.com/2yjojec.png

sirlaughsalot

09-29-2008, 07:39 PM

so in this same way does .59999... equal .6?

Torrent of Flame

09-29-2008, 07:42 PM

Probably, but it would be harder to make that proof.

TViYH

09-29-2008, 08:57 PM

Yes, .59999... = 6. Because, you can't go from 6 to 5.999999..

boberman

09-29-2008, 11:05 PM

there are 101 proofs that it is, in fact, equal to 1. If you don't believe it, then give me a mathematical counter example which shows that it is not equal to one.

My favorite is assume that

x = .9999999..... Now times both sides by 10 to get

10x = 9.999999999.....

and subtract 1 x from both sides to get

9x = 9

divide by 9...

x = 1

Please, if you can see where I made a mistake I would love for you to point it out, however if you just want to say that it is different because you lack the understanding of what infinite really means, then don't bother posting.

Death12652

09-29-2008, 11:28 PM

wow, no offense but we sound like total geeks when we say stuff like this but i guess half the people here that are 30 or under will probably become very rich, a sweet job, or they won't leave the forum and live with there mom the rest of there lives. Buy the way i agree with Thevoiceinyorhead guy.

Brain

09-30-2008, 12:13 AM

sweet

TViYH

09-30-2008, 12:23 AM

if (not(Brain=Spam)) then

begin

WriteLn('The sky is falling!');

end

else

WriteLn('Brain = Phail.');

Brain

09-30-2008, 12:26 AM

if (not(Brain=Spam)) then

begin

WriteLn('The sky is falling!');

end

else

WriteLn('Brain = Phail.');

spam where postcounts dont add up eh?

TViYH

09-30-2008, 12:42 AM

My postcounts add up. I've been here since July of last year.

EDIT: April, sorry.

Brain

09-30-2008, 12:49 AM

My postcounts add up. I've been here since July of last year.

EDIT: April, sorry.

No no no no

This section, posts don't add to your postcount.

TViYH

09-30-2008, 01:04 AM

Uhm. Pretty sure they do?

EDIT:

Ahh. No they don't. lol.

Brain

09-30-2008, 01:15 AM

Yes I know, thats what it says in the first post...thats what it says in the sticky in this section...:rolleyes:

sirlaughsalot

09-30-2008, 03:00 AM

pwnt is all i can say

spam

Heavenzeyez1

09-30-2008, 04:02 AM

Spamz0r, TheVoiceInYourHead = Failed, :D

~Eerik~

n3ss3s

09-30-2008, 06:59 AM

I can't remember what the full theory was (this is another thing), but it was something like that let's say value A, will never be 1 because it has to go through infinite 'subpoints' :(

Santa_Clause

09-30-2008, 09:31 AM

Wikipedia gives several proofs:

http://i34.tinypic.com/10eki1u.png

http://i34.tinypic.com/2ylqjqh.png

http://i36.tinypic.com/2yjojec.png

All the proofs are incorrect, due to incorrect implementation of the method used to find the fraction of a recurring decimal. Pseudomathematics, in my opinion.

EvilChicken!

09-30-2008, 10:31 AM

0.999..n will NEVER be equal to one.

The last decimal will allways make the difference.

And, I LOL'ed at that formula. Santy is right, the used the formula wrongly.

TViYH

09-30-2008, 11:20 AM

But there is no last number.

And no, they used the formula correctly.

AzulDrake

09-30-2008, 11:27 AM

At least you people understand the formula. I suck at maths so I just let my eyes glaze over when ever I see formulas :)

Santa_Clause

09-30-2008, 11:40 AM

But there is no last number.

And no, they used the formula correctly.

There's no last number in 0.99999999999... but there's a last number in 1.0. That just proves that it's incorrect.

And no, the formula is used incorrectly. When you use it to find the fraction of a recurring decimal, you have to isolate the non-recurring part from the recurring part, by multiplying by an integer multiple of 10. In 0.999999... the recurring and non-recurring can not be separated, and so the formula is not usable.

Zyt3x

09-30-2008, 11:43 AM

No. 0.999999... does not equal to 1.

Try in scar.

begin

WriteLn(BoolToStr(0.999999999999 = 1));

end.

Santa_Clause

09-30-2008, 11:46 AM

No. 0.999999... does not equal to 1.

Try in scar.

begin

WriteLn(BoolToStr(0.999999999999 = 1));

end.

That's not suitable either...because SCAR doesn't let you declare recurring decimals :p

nielsie95

09-30-2008, 11:47 AM

Yea, try in scar :p

program New;

var

i: Extended;

begin

i := 0.9999999999999999;

WriteLn(FloatToStr(i));

end.

Santa_Clause

09-30-2008, 11:53 AM

SCAR automatically adds 1 to the last decimal place.

Program New;

Var

I : Extended;

Begin

I := 0.9999999999999999;

WriteLn(FloatToStr(I - 0.1111111111111111));

End.

nielsie95

09-30-2008, 11:55 AM

It does that because it thinks the 0.999~ is one.

program New;

var

i : Extended;

begin

i := 0.99999999999;

WriteLn(FloatToStr(i - 0.11111111111));

end.

boberman

09-30-2008, 02:34 PM

All the proofs are incorrect, due to incorrect implementation of the method used to find the fraction of a recurring decimal. Pseudomathematics, in my opinion.

Ok, prove the proofs wrong. There was more then one there. Give me a counter example that proves there is a difference. especially the 10x It is a very common way of finding out the fraction of a repeating number. For example .333333... = x, 10x = 3.333333...., 9x = 3, x = 1/3. Gee, it works with that case perfectly. In fact, it works with every case perfectly as long as it is implemented correctly.

All of the math world has accepted .99999... = 1 as true. If you have taken calculus you know this. If you want to say it is not true then You need to provide an example which shows a difference between the two. If you can't provide one then your opinion of it being psuedomath is a wrong one.

Heres an easy way to explain this problem verbally. .9999... is infinitely close to 1. Because it is infinitely close, there is no difference in the two numbers, and now difference can be give. But wait, you may say, what about 0.0...01 Heres the problem with that, how many zeros are there? An infinite amount you say? Well then, that 1 doesn't exist because there will never be an end to the number of zeros. So as it turns out the difference between 1 and 0.99999.... is in fact 0.

Don't believe me? Ok take 1, and take .99999.... How do you get the difference of two numbers? You subtract the one from the other. So 1 - 0.99999... Do that one until you pound it through you head that there is no difference. If you somehow magically put a 1 at the end, you haven't written enough 0's.

Brain

09-30-2008, 03:52 PM

My math teacher said that 0.999999999999..........=1

My college math teacher, I guess I should say professor.

With a Ph.D in mathematics....

TViYH

09-30-2008, 06:51 PM

It does in fact prove that it is 1.

If you can't go from .9999... to 1, then how is it a different number?

It does in fact prove that it is 1.

If you can't go from .9999... to 1, then how is it a different number?

The answer is, "it's not". There's such a minuscule difference, that they are literally the same.

If you have two identical twins, you might say "they're exactly the same!", but there will always be an unnoticeable difference.

TViYH

09-30-2008, 08:42 PM

There is no difference between .99999... and 1, .555555 and .6, etc.

boberman

09-30-2008, 08:51 PM

There is no difference between .99999... and 1, .555555 and .6, etc.

.5555... is not equal to .6, it is equal to .55555... .5999999... is equal to .6

The answer is, "it's not". There's such a minuscule difference, that they are literally the same.

If you have two identical twins, you might say "they're exactly the same!", but there will always be an unnoticeable difference.

Your analogy is broken. You could, by the same logic, argue that x = 1 and y = 1 is really a different 1 because you are using x and y, therefor there is a difference.

As previously stated, the difference is 0, not unnoticeably small, but 0. Until you stop looking at infinity as finite you'll never agree, but the fact of the matter is that infinity is not finite, it is, well, infinite. There is no difference (see my previous post).

BazzBarrett

09-30-2008, 09:35 PM

the only true way for me to discribe it is .9 recuring is < 1 and is > 0.9 recuring altough maths tells me:

x = 0.9'

10x = 9.9'

9x = 9

9/9 = 1/1 = 1 :confused:

but look at it algabraicly ;)

y = .9'

x = y

10x = 10y

10x - 1x = 10y - y

9x = 9y

x = y

y = .9' so x = .9'

i hope ive confused enough people XD

TViYH

09-30-2008, 09:44 PM

Exactly right boberman.

Infinite does not end.

Which is why it's expressed as a loop:

∞

It has no beginning, nor end.

boberman

09-30-2008, 09:45 PM

the only true way for me to discribe it is .9 recuring is < 1 and is > 0.9 recuring altough maths tells me:

x = 0.9'

10x = 9.9'

9x = 9

9/9 = 1/1 = 1 :confused:

but look at it algabraicly ;)

y = .9'

x = y

10x = 10y

10x - 1x = 10y - y

9x = 9y

x = y

y = .9' so x = .9'

i hope ive confused enough people XD

your "algabraic" proof is nothing more then saying "x = y", "x = .9999.." so y = .99999..

It proves nothing. In order to prove that .99999 is not 1 you need to use the value in a situation that give a different result then if you use 1. Good luck trying to find one.

TViYH

09-30-2008, 09:48 PM

http://polymathematics.typepad.com/photos/uncategorized/9s_algebra

EvilChicken!

09-30-2008, 11:20 PM

http://polymathematics.typepad.com/photos/uncategorized/9s_algebra

x = 0.999 ..n

9x = 9 * 0.999 ..n

9x = 8,999[..]1

And this was taken from wikipedia?

Hmm.

I'm really stupid, and EVEN I found it to be wrong.

Gah.

TViYH

09-30-2008, 11:22 PM

You obviously didn't use an infinite number -.-

boberman

09-30-2008, 11:26 PM

x = 0.999 ..n

9x = 9 * 0.999 ..n

9x = 8,91

And this was taken from wikipedia?

Hmm.

I'm really stupid, and EVEN I found it to be wrong.

Gah.

Yes, yes you are dumb... 9 * .99999 is not equal to 8.9991 but 8.999999... Gee, that looks familiar. You could argue that there is a one on the end, but since it is infinite the 1 is never presented there (yay infinity). Now, since 10x does equal 9.999.... and 9x equals 8.999999.... and also 9 (as proven before using subtraction...). Well, thanks for yet another proof that .9999... = 1. Good job!

R0b0t1

10-01-2008, 12:45 AM

Anything equals itself. Why would it equal something different?

josh81193

10-01-2008, 01:46 AM

im with r0b0t. something cant equal something else, thats just not how it works!

1x = 2x ? NO unless x = 0

TViYH

10-01-2008, 02:04 AM

Yes it can.

To go from 1 to .9999..., you simply can't do it. Therefore, it is the same thing.

josh81193

10-01-2008, 02:16 AM

Yes it can.

To go from 1 to .9999..., you simply can't do it. Therefore, it is the same thing.

thats like saying paper = plastic, because you cant change one to another..

TViYH

10-01-2008, 02:19 AM

Paper being compared to plastic has nothing to do with this conversation.

In the field of mathematics, you can't go from .99999... to 1.

Unless you can prove me otherwise, they are the same number.

Just ask any polynomial expert, mathematics professor, anyone who deals with polynomial math on a daily basis.

boberman

10-01-2008, 02:58 AM

Paper being compared to plastic has nothing to do with this conversation.

In the field of mathematics, you can't go from .99999... to 1.

Unless you can prove me otherwise, they are the same number.

Just ask any polynomial expert, mathematics professor, anyone who deals with polynomial math on a daily basis.

Amen. Argue all you like, .9999... = 1. End of story. There are many proofs out there but ultimately, if you have had math that touches calculus at all, then you should know that 0.999... = 1. You won't find anyone with a higher level knowledge of math that will say otherwise because it is like saying "Yeah, I know nothing about the all the math that I have done."

:f: These are fun just because the average joe just doesn't want to accept that there are two ways to write the same number.

bullzeye95

10-01-2008, 03:13 AM

:f: These are fun just because the average joe just doesn't want to accept that there are two ways to write the same number.

No, I don't accept it because I think the "laws" of math are exploited to come to this decision...

boberman

10-01-2008, 03:23 AM

No, I don't accept it because I think the "laws" of math are exploited to come to this decision...

lol, you make it sound like a moral crime. Sorry its not, its math pure and simple.

Tell me, what law would you propose so this crime doesn't take place? Ignore infinity? Well there goes calculus...

tank phobia

10-01-2008, 10:12 AM

The inner nerd in me sparked to life when I read the title! Then died again as I realised the proofs were already posted. :(

No argument .999...... = 1 as the proof has shown, santa nicely done trying to trick us with your "recurring decimal" rubbish, which is exactly what it is... the proof is valid.

h4x0r@1337ne55

10-01-2008, 02:47 PM

Im on hoilidays, this post made my head spin i get enough maths already. I think ill leave this 1 up to you guys to solve.

Markus

10-01-2008, 06:32 PM

The question is, what happens if you do 0,99999*10? Will the infinity become one shorter, or will the infinity create a new digit or what?

TViYH

10-01-2008, 07:13 PM

.9^ * 10 is 9.9^

const

InfiniteSymbol = '^';

boberman

10-01-2008, 11:07 PM

The question is, what happens if you do 0,99999*10? Will the infinity become one shorter, or will the infinity create a new digit or what?

lol, if you think that infinity can be one shorter then you truly don't understand it. infinity - 1 == infinity * 10. There is no difference. What does matter is how fast a function goes to infinity, but that's another topic.

Santa_Clause

10-02-2008, 01:10 AM

Amen. Argue all you like, .9999... = 1. End of story. There are many proofs out there but ultimately, if you have had math that touches calculus at all, then you should know that 0.999... = 1. You won't find anyone with a higher level knowledge of math that will say otherwise because it is like saying "Yeah, I know nothing about the all the math that I have done."

:f: These are fun just because the average joe just doesn't want to accept that there are two ways to write the same number.

Two ways to write the same number? Are you drunk? And calling us average Joes? I'd really get an ego-check if I were you.

By the way, stop mentioning people who might have done calculus...because I have done calculus, and I can assure you that I'm more knowledgeable in it than you are.

No, I don't accept it because I think the "laws" of math are exploited to come to this decision...

Pseudomathematics, exactly my point.

The inner nerd in me sparked to life when I read the title! Then died again as I realised the proofs were already posted. :(

No argument .999...... = 1 as the proof has shown, santa nicely done trying to trick us with your "recurring decimal" rubbish, which is exactly what it is... the proof is valid.

What proof? Multiplying by 10 and then subtracting? The proof is invalid. There's a difference, but it can't be written on paper. Do you so-called geniuses feel happy now?

TViYH

10-02-2008, 01:12 AM

There is not a difference.

Show me an equation to go from .999... to 1.

Exactly. There is no difference.

Santa_Clause

10-02-2008, 01:14 AM

There is not a difference.

Show me an equation to go from .999... to 1.

Exactly. There is no difference.

Did you read what I said? It can't be written on paper, but there has to be a difference.

TViYH

10-02-2008, 01:16 AM

If there was a difference, then it could be written on paper.

The difference between 5 and 6 is 1.

The difference between .999...and 1 is 0, simply because you can't go from 1 to .9999....

Santa_Clause

10-02-2008, 01:24 AM

If there was a difference, then it could be written on paper.

The difference between 5 and 6 is 1.

The difference between .999...and 1 is 0, simply because you can't go from 1 to .9999....

If there's a difference then it can be written on paper? Right...

So how do I write 0.9999, with infinite 9's? Add a dot on top of the first 9? Great. I'll add two dots on top of the second 0 in 0.01, symbolising infinite 0's. Agree?

TViYH

10-02-2008, 01:32 AM

but you can't have an infinite number followed by a number.

Because the 0's would never end, not allowing the 1 to show up.

Infinite means never ending. It can't be followed by a number, since it will never end.

Codys_Pur3

10-02-2008, 01:42 AM

Spam Spam General Dump =d

Codys_Pur3

10-02-2008, 01:43 AM

i dont understand this thread =[

boberman

10-02-2008, 01:54 AM

Two ways to write the same number? Are you drunk? And calling us average Joes? I'd really get an ego-check if I were you.

By the way, stop mentioning people who might have done calculus...because I have done calculus, and I can assure you that I'm more knowledgeable in it than you are.

Pseudomathematics, exactly my point.

What proof? Multiplying by 10 and then subtracting? The proof is invalid. There's a difference, but it can't be written on paper. Do you so-called geniuses feel happy now?

1. Lol, and I can almost absolutely assure you that you aren't more knowledgeable in math. I am near a math minor at Uni.. Gee, I just might know something about math....

2. You say I am egotistical, yet you are the one that is saying that pretty much the entire math world is wrong without providing any proof what so ever, except for saying "It feels wrong, there must be a difference." Guess what, there isn't one.

3. I say average joes because most people here are under 16. Yes there are a lot of accomplished 16 yo's, some may even have a better understanding of math then the average joe, but most have not had the math classes/opportunities that the average joe of 21+ has had. In essence, I am treating 16 yo's as 21 yo's, I do have a fair amount of respect for them (if you are not 21, that's fine, you are probably an above average joe).

4. You say this is all Puesdomathmatics, How so? Because what you see or feel can't be written on paper all the sudden your logic becomes infallible? Sorry, but sometime the counter intuitive answer is the right one. I question your calculus because you should know that the right answer can't always be intuitively understood. I question your calculus because the 1 = .999... proof is one that is done in most pre-calculus classes and is a proof that should have been reaffirmed by any good calculus teacher. The reason behind this is because this proof teaches us an essential understanding of what infinity really is.

Yes, I feel somewhat knowledgeable about mathematics, but that would be because I have taken several upper-level math courses. I have proven my argument and the only response you can come back with is "It can't be disproven on paper" Well, guess what, That's baloney. Had you taken (and done well at) a calculus then you would have known that from the countless proofs that you should have done.

So again I ask, disprove it. Show where any math rule was broken. But again I warn you, everyone with a PhD in mathematics accepts that .9999...=1, so it isn't just some random guy on the internet telling you this, it is the entire mathematics community as a whole.

I have never met a person in real life that did well at calculus that would argue that .9999... != 1. I have only ever met people that didn't understand the concept of infinity (and hence don't understand calculus) that would argue against it.

Brain

10-02-2008, 02:04 AM

I agree with boberman, as I stated earlier, my math professor with PhD in mathematics, says that 0.999.... is in fact equal to one.

TViYH

10-02-2008, 02:05 AM

Omg. Boberman. You are t3h secks.

If I knew where you are, not only would I shake your hand.

I would lick your ear.

mixster

10-03-2008, 04:00 PM

I'm thinking that infinite is confined by time. In the the time it takes 0.(infinite)9 to reach 0.99999, 9.(infinite)9 would only reach 9.9999, meaning that the difference is 1 div (10 ^ infinite). For each loop through of infinity, the difference between the two is decreased by div 10, but is still a difference. If infinite is not constrained by time, then this is irrelevant, but is still my opinion none the less.

pini3000

10-03-2008, 05:41 PM

Well I am a science dude. Anything related to Chemistry, Biology (to an extent physics as the entire concept of universal membranes is amazing) is what I can answer.

I did do extended/further maths but that was all Hyperbolic functions and rubbish. In tis case, I would just stick two dots about the number following the decimal lol

sirlaughsalot

10-03-2008, 06:09 PM

Okay, so this is accepted by the math world, but it is based upon, since .999... never doesnt reach 1, it must be the same thing? that doesnt make sense to me, but if it is accepted then it must be true

TViYH

10-03-2008, 06:53 PM

It's not that it never reaches it.

It's that you can't go from 1 to .999...

boberman

10-03-2008, 06:56 PM

Okay, so this is accepted by the math world, but it is based upon, since .999... never doesnt reach 1, it must be the same thing? that doesnt make sense to me, but if it is accepted then it must be true

It is based on the fact that there is no difference between 1 and .999... . Difference is the remainder of the subtraction of two numbers. So if you take 1 and subtract .999... the remainder is 0. When you have 0 difference between two numbers, they must be the same number. The proof that this is so have been listed several times in this thread.

I'm thinking that infinite is confined by time. In the the time it takes 0.(infinite)9 to reach 0.99999, 9.(infinite)9 would only reach 9.9999, meaning that the difference is 1 div (10 ^ infinite). For each loop through of infinity, the difference between the two is decreased by div 10, but is still a difference. If infinite is not constrained by time, then this is irrelevant, but is still my opinion none the less.

Infinity and time are two completely separate and different concepts. Time doesn't effect infinity and infinity doesn't effect time. Its like saying the sky is blue because it's October. Or saying apples taste good because bananas are yellow.

.999... isn't propagating at any speed, it is already infinitely long by definition.

atlanta788

10-14-2008, 01:22 AM

???

dinkerdude

10-14-2008, 08:54 AM

:mad: :redface: :rolleyes: :bart: :) :(h): :p :f: lol i dont understand:sasmokin: :garfield:

TViYH

10-14-2008, 06:59 PM

Wow.

That was completely unnecessary spam.

But, I guess this might be too.

Cstrike

10-14-2008, 09:53 PM

Technically at infinity looking from a physics standpoint, it would equal one. Theoretically it wouldn't, but in any real life thing... it would SLOWLY approach the point that the number would be so close to 1; it would be indistinguishable.

boberman

10-15-2008, 12:17 AM

Technically at infinity looking from a physics standpoint, it would equal one. Theoretically it wouldn't, but in any real life thing... it would SLOWLY approach the point that the number would be so close to 1; it would be indistinguishable.

What on earth are you talking about? .9999.. is not a real life thing, it is a concept. The concept is that there are an infinite number of 9's following the decimal point, not that some fairy is writing 9's at some set speed, they are already there, the entire infinite amount of them.

It has nothing to do with physics, at all. This a math problem plane and simple.

Magiic

10-15-2008, 05:21 PM

.999999 reccuring rounded up =1 (my infinite reasoning)

TViYH

10-15-2008, 05:33 PM

You can't round .99999... up, because you can't add infinite 0's after a decimal, and then a 1.

boberman

10-15-2008, 07:03 PM

.999999 reccuring rounded up =1 (my infinite reasoning)

Thats like saying 2 rounded up = 2. No, it isn't, 2 = 2, no rounding needed. Same with .99999... It is equal to one, not close to one, not almost one. It is one.

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