I cant belevie ppl cant put this through their heads

[emmdoubleew]

that .999... and 1 are the same number.

I just spent 10 minutes areguin with someone -_- , and the things he said...

[tompilk]

i dont get this... im sorry.
If you multiply a third (0.3333 etc) by three you get 0.999 etc., so it must be one... it has to be...
Ive been thinkinbg since primary school how this can be and you've made me realise that 0.999etc is 1.
Im still not completely convinced, because thats like saying its the same as 0.9999recurring8 which would mean that 0 is the same as one, and that every number was every other number.
Ah, but no because it isnt recurring! Ah, I see... i solved it in my mind...
Thanks,
Tom

[emmdoubleew]

i dont get this... im sorry.
If you multiply a third (0.3333 etc) by three you get 0.999 etc., so it must be one... it has to be...
Ive been thinkinbg since primary school how this can be and you've made me realise that 0.999etc is 1.
Im still not completely convinced, because thats like saying its the same as 0.9999recurring8 which would mean that 0 is the same as one, and that every number was every other number.
Ah, but no because it isnt recurring! Ah, I see... i solved it in my mind...
Thanks,
Tom

Hahhaa, I have to admit that post is a little strange Tom, but I'm gald you figured it out on your own . If you want I can provide many other posts.

The truth is you'll never encouter .999.... repeating in your life, because 1 is the much more common form.

[lau]

this is blasphamacrap.    .99 isn't 1, it's just incredibly close to one. But if your in real life its so close that it doesn't matter, but the fact still is that it is not one.

[pianistimo]

are we talking about gas prices.  i'll take .99.  that's the way i'm living my life now.  counting pennies.  i come out of the grocery store after quibbling about the exact price of the turkey - only to check the entire receipt just in case something was accidentally input twice.  these things are important if u are interested in pennies.  but, as i is - i have so many pennies that i have to use them at mc donald's.  they hate me counting - so i try to count ahead of time.  actually i need to get a roller.  then i'd just hand them the rolled tens. 

maybe they'll do away with pennies completely.  i heard on the news it's part of a government agenda (so people can't save money) just kidding. 

what u really REALLY have to watch is those hidden charges in everything.  i mean - i found out from a friend that he took his family out to dinner - only to find out that when u have a party of 20 or something at this one restaurant - they include the tip AUTOmatically.  then, after tipping the second time - at home he looked at the bill and sure enough - he had already tipped.  so , his wife calls the restaurant and they say they'll send him a check for the extra tip.  they haven't received it yet.

read the fine print.  use coupons (i'm finding i've been too lazy).  one lady ahead of me in the check out line got her groceries for $30. after a stack of coupons.  i thought, hmm.  something to do.  of course, u can't do that at a farmers market - but that's another cheap way to eat good.

saving money is now my number one priority.  my son is really disappointed he HAS to do driving school before we let him get a license.  i said, 'do u really think i'd give up the student driving discount for having gone thru driving school?'

[shoenberg3]

the last two posts completely missed the original post's point... i really hope it is for the sake of comedic genius..

[emmdoubleew]

this is blasphamacrap.    .99 isn't 1, it's just incredibly close to one. But if your in real life its so close that it doesn't matter, but the fact still is that it is not one.

I'm gonna give you the benefit of the doubt and assume you're joking.

However if you aren't, show me a mathematical proof that they are different, and I will show you 5 or 6 that they are the exact same.

are we talking about gas prices.  i'll take .99.  that's the way i'm living my life now.  counting pennies.  i come out of the grocery store after quibbling about the exact price of the turkey - only to check the entire receipt just in case something was accidentally input twice.  these things are important if u are interested in pennies.  but, as i is - i have so many pennies that i have to use them at mc donald's.  they hate me counting - so i try to count ahead of time.  actually i need to get a roller.  then i'd just hand them the rolled tens. 

maybe they'll do away with pennies completely.  i heard on the news it's part of a government agenda (so people can't save money) just kidding. 

what u really REALLY have to watch is those hidden charges in everything.  i mean - i found out from a friend that he took his family out to dinner - only to find out that when u have a party of 20 or something at this one restaurant - they include the tip AUTOmatically.  then, after tipping the second time - at home he looked at the bill and sure enough - he had already tipped.  so , his wife calls the restaurant and they say they'll send him a check for the extra tip.  they haven't received it yet.

read the fine print.  use coupons (i'm finding i've been too lazy).  one lady ahead of me in the check out line got her groceries for $30. after a stack of coupons.  i thought, hmm.  something to do.  of course, u can't do that at a farmers market - but that's another cheap way to eat good.

saving money is now my number one priority.  my son is really disappointed he HAS to do driving school before we let him get a license.  i said, 'do u really think i'd give up the student driving discount for having gone thru driving school?'

nvm, i said something mean.

[steveie986]

.99999... (the ... means repeating ad infinitum) is equal to 1.

Facts:
A. 1/9 * 9 = 1
B. 1/9 = .111111...

Thus, .111111... * 9 = .999999... = 1, by A. and B.

[pianistimo]

well, emdoubleeww, i've wondered that point myself.  it does hinder spontenaity, if that's what u mean.  u can't just enjoy life without wondering what the price is.  i mean, if it has .99 ur saving a penny.

sometimes, i have to try not to be so perfectionistic.  it's a disorder of sorts.  i can't say i've gotten to the obsessive compulsive high scale like that woman on tv that is so scared of germs she picks her clothing out with her bare feet (toes) if she's touched a doorknob.  i think that was it.  anyway - she also goes around cleaning everything (several times).  i'm sort of compulsive for an hour or so - and then i think - what's the dif.  it's going to get messed up again.  that's when i come on pianostreet.

[shoenberg3]

legendary CG by pianitismo, *. nearly doofus level (if you remember him from chopfiles)

[emmdoubleew]

i'm sort of compulsive for an hour or so - and then i think - what's the dif.  it's going to get messed up again.  that's when i come on pianostreet.

Well, I'm glad you do because you bring us wonderful insight.

[pianistimo]

well, i will leave with that nice compliment (or, hmm. think about it and ponder).  son wants to play games.

[lau]

I'm gonna give you the benefit of the doubt and assume you're joking.

However if you aren't, show me a mathematical proof that they are different, and I will show you 5 or 6 that they are the exact same.

Coca-Cola
32 fluid ounces caramel
32 fluid ounces lime juice
16 fluid ounces glycerin
12 fluid ounces 95% alcohol
12 fluid ounces Cola Flavor Base (recipe below)
Caffeine solution (2 ounces caffeine in 10 fluid ounces water)
2 fluid ounces vanilla extract

These are mixed to produce 1 gallon of cola flavor. Four ounces of this cola flavor plus .5 fluid ounces of diluted phosphoric acid (one part 85% phosphoric acid to seven parts water), are used to flavor a gallon of high fructose corn syrup.

Cola Flavor Base

This is the secret stuff.

46.8 g. lemon oil
14.2 g. orange oil
14.2 g lime oil
10.7 g cinnamon oil
3.5 g nutmeg oil

[musik_man]

.99999999... does not exist.  It (along with infinity) is merely a convenient concept.

.99999... (the ... means repeating ad infinitum) is equal to 1.

Facts:
A. 1/9 * 9 = 1
B. 1/9 = .111111...

Thus, .111111... * 9 = .999999... = 1, by A. and B.

1/9 =/= .11111111...
As you add more digits .1111.... approaches 1/9, but no matter how far you go, it will never equal it.


Do you not notice that in proving .999...=1 you claim that .11111=1/9?  Anyone who disagrees with the first would obviously dispute the second, so you can hardly take it as a given.  You first need to prove that 1/9=.11111

[steveie986]

.99999999... does not exist.  It (along with infinity) is merely a convenient concept.

1/9 =/= .11111111...
As you add more digits .1111.... approaches 1/9, but no matter how far you go, it will never equal it.


Do you not notice that in proving .999...=1 you claim that .11111=1/9?  Anyone who disagrees with the first would obviously dispute the second, so you can hardly take it as a given.  You first need to prove that 1/9=.11111

I did not claim that .11111 = 1/9. Rather, I claimed that .11111... = 1/9. It is true that as you add more digits to .1111... it will never approach 1/9, but the "..." means "an infinite number" of digits past the decimal point.

[musik_man]

I did not claim that .11111 = 1/9. Rather, I claimed that .11111... = 1/9. It is true that as you add more digits to .1111... it will never approach 1/9, but the "..." means "an infinite number" of digits past the decimal point.

I meant .1111...  I just forgot to put the elipse.  Would you care to prove that .11111...=1/9?  Cause I don't accept that as a fact, seeing as how .1111... doesn't exist.

[prometheus]

You can't have an infinite amount of 9's. I guess that is the problem. .999~ would be 1 part of 1 and .333~ would be 1 one part of 3 (or 1/1th and 1/3rd). A number can't go on endlessly. You have to round down somewhere. That's why there are fractions.

I guess it is just that mathematicians are allowed a certain flexibility with abstract concepts due to axioms. They are allowed to have an infinite number. I mean, in a sence expressing 1/3rd as a number would be an infinite number. It is called a rational number. Math even has Imaginary number.

These things are not logical and cannot be proven. They are just a result of the axioms math presupposes because it makes math usable and efficient.

Infinity does not exist. This is also why God cannot be omniscent. It is a logical contradiction.
Math even allows you to add numbers to infinite. The infinite number then does become larger, but not more or less infinite that it already is. At least I think that is what mathematicians have accepted to be the case.

So, yes. This is what mathematicians accept as true. But you cannot prove it.

[musik_man]

You can't have an infinite amount of 9's. I guess that is the problem. .999~ would be 1 part of 1 and .333~ would be 1 one part of 3 (or 1/1th and 1/3rd). A number can't go on endlessly. You have to round down somewhere. That's why there are fractions.

I guess it is just that mathematicians are allowed a certain flexibility with abstract concepts due to axioms. They are allowed to have an infinite number. I mean, in a sence expressing 1/3rd as a number would be an infinite number. It is called a rational number. Math even has Imaginary number.

These things are not logical and cannot be proven. They are just a result of the axioms math presupposes because it makes math usable and efficient.

Infinity does not exist. This is also why God cannot be omniscent. It is a logical contradiction.
Math even allows you to add numbers to infinite. The infinite number then does become larger, but not more or less infinite that it already is. At least I think that is what mathematicians have accepted to be the case.

So, yes. This is what mathematicians accept as true. But you cannot prove it.

 

[steveie986]

The fact that .1111... = 1/9 is not "provable." It is simply based on axioms about the nature of rational numbers.

If 0.1111... does not "exist" (whatever that means), then 1/9 does not "exist" either. Both point to some entirely abstract entity which we can refer to by two equivalent labels: 1/9 and .1111....

[pianistimo]

i'm back.  although, i must confess, i understand lau better than the last posts.  if i follow the math - it would be that 1/9 TURNs into one after a cycle.  so, there's an element of very close that makes it appear moreso after enough repetitions.  like, when ur told something is so - and u hear it enough times.

[emmdoubleew]

.99999999... does not exist.  It (along with infinity) is merely a convenient concept.

All numbers are concepts. Some numbers, like 1, have stronger links to reality than others, but we are looking at mathematics here, not the real world. If you're going to throw away numbers which can't concretely exist, then you're throwing away pi, e, i, zero, and, frankly, almost all of mathematics.

1/9 =/= .11111111...
As you add more digits .1111.... approaches 1/9, but no matter how far you go, it will never equal it.

Silly, you can't "add more digits" to a static number.
.111... is the decimal representation of 1/9, just as 1.000... is the decimal representation of 1/1.

However if you are dissatisfied with his proof, I will be glad to offer you another one:
      x = 0.9999...

Multiply both sides by ten:

    10x = 9.9999...

Subtract x from both sides:

10x - x = 9.9999... - 0.9999...
     9x = 9.0000...

Divide by nine:

      x = 1.0000...

And another one:
0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

          = 9·0.1 + 9·0.01 + 9·0.001 + 9·0.0001 + ...

          = 9·10-1 + 9·10-2 + 9·10-3 + 9·10-4 + ...

            n=∞
          =  Σ 9·10-n
            n=1

                n=N
         := lim  Σ  9·10-n
            N→∞ n=1

          = lim ( 1 - 10-N )
            N→∞

          = lim 1 - lim 10-N
            N→∞     N→∞

          = 1 - 0
          = 1

And another one:
0.9999... ≤ 1.

Assume

0.9999... ≠ 1 (*).

Then

0.9999... < 1,

so there must be some positive number P so that

0.9999... + P = 1.

But for ANY positive P,

0.9999... + P > 1,

which is a contradiction, and definitely wrong. Therefore we are forced to conclude that the assumption (*) was incorrect, that is:

0.9999... = 1


One more perhaps?
Observe that the limit of the sequence

0.9
0.99
0.999
0.9999
0.99999
...

is

0.9999...

That is, the sequence gets closer and closer to 0.9999..., in fact, infinitely close.

But the sequence also gets closer and closer to 1.0000..., in fact, infinitely close. So 1.0000... is a limit of this sequence too.

But a sequence can only have one limit, so 0.9999... and 1.0000... must be the same.

[emmdoubleew]

Infinity does not exist. This is also why God cannot be omniscent. It is a logical contradiction.

I don't remember anyone saying anything about infinity. Infinity is not a number, it is a concept. 0.999... is a number that is part of the set of all real numbers.

So, yes. This is what mathematicians accept as true. But you cannot prove it.

As a matter of fact i have provided 4 completely foolproof proves of it.

[steveie986]

Observe that the limit of the sequence

0.9
0.99
0.999
0.9999
0.99999
...

is

0.9999...

That is, the sequence gets closer and closer to 0.9999..., in fact, infinitely close.

But the sequence also gets closer and closer to 1.0000..., in fact, infinitely close. So 1.0000... is a limit of this sequence too.

But a sequence can only have one limit, so 0.9999... and 1.0000... must be the same.

I liked this one.

[steveie986]

However if you are dissatisfied with his proof, I will be glad to offer you another one:
      x = 0.9999...

Multiply both sides by ten:

    10x = 9.9999...

Subtract x from both sides:

10x - x = 9.9999... - 0.9999...
     9x = 9.0000...

Divide by nine:

      x = 1.0000...

But I can argue that 10x - x = 9x = 8.999...?

[steveie986]

https://www.math.fau.edu/Richman/HTML/999.htm

[emmdoubleew]

But I can argue that 10x - x = 9x = 8.999...?

You'd be assuming that .9999... = 1 though, which was what was being proven.

But yes, now that it has been proven, you could. It wouldn't make a difference though because having proven this we also know that 8.999... = 9

[musik_man]

The fact that .1111... = 1/9 is not "provable." It is simply based on axioms about the nature of rational numbers.

If 0.1111... does not "exist" (whatever that means), then 1/9 does not "exist" either. Both point to some entirely abstract entity which we can refer to by two equivalent labels: 1/9 and .1111....

If you use .11111... as a proxy for 1/9 because it is convenient I have no quarrel. 

emmdoubleew, I can't agree with any of the proofs you use.  The first assumes you can multiply an abstraction like .999.... with a real number.  The second shows that the limit of the series used to give .999.. approaches 1, which I'll readily conceed.   The third once again uses .1111... as a number instead of an abstraction.  The  last one I think fundamentally misinterprets what a limit(or convergence) is about.  As you take the function f(x)=1/x to infinity, it gets infinitely close to f(x)=0, but I doubt you'd be silly enough to claim that f(infinity)=0.  As I said before, infinity is only a nice and convenient concept.  .9999... doesn't exist except as an abstraction. 

[steveie986]

If you use .11111... as a proxy for 1/9 because it is convenient I have no quarrel. 

emmdoubleew, I can't agree with any of the proofs you use.  The first assumes you can multiply an abstraction like .999.... with a real number.  The second shows that the limit of the series used to give .999.. approaches 1, which I'll readily conceed.   The third once again uses .1111... as a number instead of an abstraction.  The  last one I think fundamentally misinterprets what a limit(or convergence) is about.  As you take the function f(x)=1/x to infinity, it gets infinitely close to f(x)=0, but I doubt you'd be silly enough to claim that f(infinity)=0.  As I said before, infinity is only a nice and convenient concept.  .9999... doesn't exist except as an abstraction. 

I'm sorry - and I don't say this very often - but I really don't think you know what you're talking about, and I think you know it too. Now, I'm not trying to be mean or hurt your feelings but I think we should just let this issue rest. If we haven't managed to convince you by our reasoning, we won't continue to argue with you. There are more important issues to tackle in life.

[musik_man]

I'm sorry - and I don't say this very often - but I really don't think you know what you're talking about, and I think you know it too. Now, I'm not trying to be mean or hurt your feelings but I think we should just let this issue rest. If we haven't managed to convince you by our reasoning, we won't continue to argue with you. There are more important issues to tackle in life.

Well, I in fact don't know that I don't know what I'm talking about, but if you want to drop the issue, it's fine by me.  I'd be hard pressed to find any issue on any subject that has less real world relevance than this.  Perhaps next time we can debate how many angels can dance on the head of a pin.

[henrah]

Perhaps next time we can debate how many angels can dance on the head of a pin.

I'd say, hhmmm.... 7 maybe? Possibly 8 if they had their wings folded in... Or only 1, if that angel is Emma Thompson

[tompilk]

Well, I in fact don't know that I don't know what I'm talking about, but if you want to drop the issue, it's fine by me.  I'd be hard pressed to find any issue on any subject that has less real world relevance than this.  Perhaps next time we can debate how many angels can dance on the head of a pin.

i think it is important to ask questions like this... where would we be if we didnt understand anything? This is totally relevant, and discussions about obscure things is generally how world breakthroughs are made...
So were at the forefront of philisophical advancements!
Tom

[musik_man]

i think it is important to ask questions like this... where would we be if we didnt understand anything? This is totally relevant, and discussions about obscure things is generally how world breakthroughs are made...
So were at the forefront of philisophical advancements!
Tom

Can you give me one real world application of this?  Or even some philisophical/metaphysical ones?

BTW the correct anwser for angels/pins is 42

[steveie986]

Can you give me one real world application of this?  Or even some philisophical/metaphysical ones?

BTW the correct anwser for angels/pins is 42

The problem that was originally raised is actually quite deep and has a long and distinguished history in the course of Western philosophy, going back to the time of Zeno of Elea (c. 490-430 BC). The problem of .999... =/!= 1 can be generalized to Zeno's Paradoxes of Motion (https://en.wikipedia.org/wiki/Zeno%27s_paradoxes). The article goes into considerable (fascinating) detail about this and related problems. Essentially, the argument of the paradoxes were not fully resolved until the development of the concept of limits in calculus in the 19th century. In the 20th century, many advancements have been made in the fields of logic and philosophy of math on issues related to infinity, infinitesimals, and set theory (Hilbert's, followed by ZFC). I have taken one university class on mathematical logic but I'm hardly the expert to discuss the finer details.

So... basically this problem is certainly "useless" from a practical, engineering perspective, but it can be easily generalized into some deep, mystifying stuff.

[johnny-boy]

$1,000,000
   X .999
$  999,000

$1,000,000
    X     1
$1,000,000

The same? Not!

John

[steveie986]

$1,000,000
   X .999
$  999,000

$1,000,000
    X     1
$1,000,000

The same? Not!

John

Surely you're joking, Mr. John?

[prometheus]

I don't remember anyone saying anything about infinity. Infinity is not a number, it is a concept. 0.999... is a number that is part of the set of all real numbers.

.999~ goes on infinitely. But the fraction 1/9 doesn't. So 9/9 is 1 but if you have an infinite amount of 9's it just looks tricky. In a sense one could argue that .999~ and 1/9 aren't the same.

Music_Man. God can't create a stone he cannot lift herself. Sure, everyone has heard this one and thinks it is silly. But really, what is omniscence? It cannot be defined. It cannot exist because it contradicts itself.

$1,000,000
   X .999
$  999,000

We are talking about .999~ which can only be expressed accurately by 9/9.

So it will be 999.~

You cannot have an amount of .999~ dollar. Just like you cannot have .111~ dollar. You don't have an infinite number or .1 and .01 and .001 and .0001 dollar coins. There is also no fraction dollar coin.

In the real world all numbers are different than in math. I mean you can also divide something in half until the end of the world and you will never be left with nothing. But in practice that makes no sense at all.

But I can argue that 10x - x = 9x = 8.999...?

9x = 8.999~
9x = 8 + 9/9

Divive both sides by 9

x = 8/9 + 9/81
x = 8/9 + 1/9
x = 9/9
x = 1

[tompilk]

$1,000,000
   X .999
$  999,000

$1,000,000
    X     1
$1,000,000

The same? Not!

John

we are talking about recurring decimals!!!
Tom

[tompilk]

The problem that was originally raised is actually quite deep and has a long and distinguished history in the course of Western philosophy, going back to the time of Zeno of Elea (c. 490-430 BC). The problem of .999... =/!= 1 can be generalized to Zeno's Paradoxes of Motion (https://en.wikipedia.org/wiki/Zeno%27s_paradoxes). The article goes into considerable (fascinating) detail about this and related problems. Essentially, the argument of the paradoxes were not fully resolved until the development of the concept of limits in calculus in the 19th century. In the 20th century, many advancements have been made in the fields of logic and philosophy of math on issues related to infinity, infinitesimals, and set theory (Hilbert's, followed by ZFC). I have taken one university class on mathematical logic but I'm hardly the expert to discuss the finer details.

So... basically this problem is certainly "useless" from a practical, engineering perspective, but it can be easily generalized into some deep, mystifying stuff.

oh... my... god...
When i was in scotland sailing I saw a bit of dirt floating around in a puddle of water and I thought to myself "At one point it is there and another it is different - but how deos it move between the individual points of time?"
OMG, I then sorted it out in my head and solved it with the continual time thingy. But i still hadn't convinced myself. That was when i was about 10... and Ive wondered ever since and that webpage proved me right! lol... anyone could have thought of that...
Zeno gets a Wiki page for something I worked out! Unfair!!!
Tom

[nicco]

So this whole thread is about 0.999... and 1 being the same number?

well, as you can see its clearly not. Claiming that they are the same is stating something that there is no answer to, because no matter how many decimals you put after the comma, you can always put one more...and then 1 more...and then a million more...so bascally you are just rounding off 0.99... to be 1, two different numbers. yes they are close, insanely unbelievably close, but they are still different. Im gonna get yelled at now  Sorry 

[musik_man]

The problem that was originally raised is actually quite deep and has a long and distinguished history in the course of Western philosophy, going back to the time of Zeno of Elea (c. 490-430 BC). The problem of .999... =/!= 1 can be generalized to Zeno's Paradoxes of Motion (https://en.wikipedia.org/wiki/Zeno%27s_paradoxes). The article goes into considerable (fascinating) detail about this and related problems. Essentially, the argument of the paradoxes were not fully resolved until the development of the concept of limits in calculus in the 19th century. In the 20th century, many advancements have been made in the fields of logic and philosophy of math on issues related to infinity, infinitesimals, and set theory (Hilbert's, followed by ZFC). I have taken one university class on mathematical logic but I'm hardly the expert to discuss the finer details.

So... basically this problem is certainly "useless" from a practical, engineering perspective, but it can be easily generalized into some deep, mystifying stuff.

You can glean as much deep and interesting stuff from those paradoxes as you can from the angel/pin question in my opinion.  Thanks for reminding me of how much I hate philosophers.

[tompilk]

how is it useless? maybe it will prove to be the meaning of life. Never dismiss something which hasn't been fully explored...
Tom

[musik_man]

how is it useless? maybe it will prove to be the meaning of life. Never dismiss something which hasn't been fully explored...
Tom

It's useless cause it's wrong.  Go test them out with some real world data.  I am able to move, and have passed people on the highway, so obviously the paradoxes are screwed up.  No one should try to find purpose in this sort of intellectual m*sturbation.

[tompilk]

Just because things don't seem realistic doesn't mean they don't exist.
Many things work in theory but not in practise - all they need is a secret or one particular bit of information...
And, what's the point in posting here if you hate it? You are free to go away and ignore it if you detest the conversation.
Please, don't use absolutes either. You can't say it's useless because it is wrong. Prove it...
Also, who says it has to work in the 'real' world to be correct? The possibilities of everything are endless... the mind is as powerful as you let it be...
"No one should try to find purpose" - why not? It's extremely interesting and as I have said, thinking and using your mind is useful just on it's own! Whatever opinion you have, declare it as your opinion and DO NOT claim things to be the truth because it could end up offending...
Tom

[johnny-boy]

Surely you're joking, Mr. John?

Here's the original post:
that .999... and 1 are the same number

They are not!  If you want to round it off to "1" that's fine with me.

.999........ no matter how far it's extended it's still going to come up short from "1".

John

[timothy42b]

It's useless cause it's wrong.  Go test them out with some real world data.  I am able to move, and have passed people on the highway, so obviously the paradoxes are screwed up.  No one should try to find purpose in this sort of intellectual m*sturbation.

It's not useless, and not a paradox.

It only appears so because of an oversimplification in the math, and the attempt to use words to describe reality instead of equations.

Math is the language of science just as notes are the language of music.  Verbal descriptions are always imprecise and sometimes, as here, confusing. 

[tompilk]

Here's the original post:
that .999... and 1 are the same number

They are not!  If you want to round it off to "1" that's fine with me.

.999........ no matter how far it's extended it's still going to come up short from "1".

John

0.999 will come to 1!!! because it is infinitly continued!

[johnny-boy]

0.999 will come to 1!!! because it is infinitly continued!

It will never become "1" because it is infinitely continued.

John

[Ruro]

Here's the original post:
that .999... and 1 are the same number

They are not!  If you want to round it off to "1" that's fine with me.

.999........ no matter how far it's extended it's still going to come up short from "1".

John

I have thought about something similar to this on several occasions, and frankly I agree with Johnny. The idea of endless numbers, steadily increasing in value but never reaching a whole number seems.... "unreal" - seems similar to asking how "wide" the Universe is; never ending? Pft, like I know.

Seems like flaw in Math in something. Hearsay: As I understand it Quantum mechanics was produced to answer the latest unexplainable theories Classic Theories couldn't explain - because they were either entirely/slightly wrong.

I know jack all about this stuff, but Imo, Math seems way to "limited" for this stuff.

0.999 will come to 1!!! because it is infinitly continued!

I'm gonna ponder on this, see if I can grasp what ya mean :/

EDIT: what, has there been an official answer to this "problem"? Or is this, to-date, and on going debate? Because if it's been solved, I'm gonna stop arguing now, hehe, since there must be proof.

[prometheus]

Quantum mechanics go back to 1905. So they aren't new.
With it the fundamental ideas changed to something totally different. But the results in math are the same on a macroscale, meaning our level of reality.

Yes, while the number .999~ goes on infinitely that doesn't mean it does not exist. It only means you cannot write it down that way. You can write down numbers like .333~ and .111~ with fractions. 1/3 and 1/9. It is clear that .999~, 9/9 and 1 come down to the same? But why would one use .999~ instead of 1?

Yes, it is a 'artifact' in our numbers system so it seems. But that is because we use a decimal system. Do you have a solution?

So with the fraction 2/3 written out as a rational number will the last number be a 6 or a 7?

[tompilk]

Quantum mechanics go back to 1905. So they aren't new.
With it the fundamental ideas changed to something totally different. But the results in math are the same on a macroscale, meaning our level of reality.

Yes, while the number .999~ goes on infinitely that doesn't mean it does not exist. It only means you cannot write it down that way. You can write down numbers like .333~ and .111~ with fractions. 1/3 and 1/9. It is clear that .999~, 9/9 and 1 come down to the same? But why would one use .999~ instead of 1?

Yes, it is a 'artifact' in our numbers system so it seems. But that is because we use a decimal system. Do you have a solution?

So with the fraction 2/3 written out as a rational number will the last number be a 6 or a 7?

well done. i like the bit about existing even though it cannot be written discussion closed. everyone kn ows a third is 0.333~, and that 3/3 = 1, so 0.999~ must be one! it only m,akes sense!
Tom