1 = 0.9999999...

[Sarka]

I'm having a mathematical debate with someone who believes 1 = 0.9999...

I personally, do not think that this is the case, even with his really terribly smart (for 14) equations:

--------------------

Let X = 0.999...

•
Then 10X = 9.999...

Subtract X from each side to give us:
•
9X = 9.999... - X

but we know that X is 0.999..., so:
•
9X = 9.999... - 0.999...
or: •
9X = 9

Divide both sides by 9:
•
X = 1

--------------------

x = 0.9999...

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

--------------------

0.9999... ≤ 1
If
0.9999... < 1
then there is some positive number P so that
0.9999... + P = 1
But for ANY positive P,
0.9999... + P > 1
which contradicts the equation in . Therefore the only possible alternative is
0.9999... = 1

--------------------

Buw how can 1 = 0.99999999...

HELP PLEASE!

[RATM_4_EVA]

I guess it has no solution

[RoadKill]

This argument is as old as the sun.

What they mean is 0.99999999... = 1.

Not 1 = 0.99999999.

Then the line gets blurry. You have an infinitely close value to 1, but you never quite have 1. Either way don't ask me.

Don't argue about this though, it's a waste of time.

[Sarka]

But since, as you say, never quite 1, then how can it equal 1?!

[Twozzok]

oh dear god, not this, please...

SA gets this so much they've made it a bannable offence to start up this discussion ¬_¬

[Sarka]

Really? I've never seen it anywher ebefore on the net, ever.

[craig]

One equals one. If your friend thinks otherwise just let him believe that.
The mathematical equations that you posted are incorrect.

[Monopolyman]

Basically, I think, everybody agrees 0.3333...=1/3, now multiply both sides by 3

1/3 x 3=1
0.3333... x 3=0.9999....

Therefore 0.9999...=1



Ah, I'm so clever

[RoadKill]

You don't really get around that much...

I search for it on the Something Awful forums (the 5th most active forum on the Internet, apparently) and it comes up many a time, with people oft-groaning from its resurrection.

[Twozzok]

You don't really get around that much...

I search for it on the Something Awful forums (the 5th most active forum on the Internet, apparently) and it comes up many a time, with people oft-groaning from its resurrection.


what are the 4 more active forums?

[RoadKill]

I dunno man, I don't remember at all...

That's the only statistic I could remember from whereever I saw it.

Either way it's the #1 for just being the awesome on the internet.

[Supergrunch]

I was about to post Monopolyman's solution, but he beat me to it.

Anyway, most mathematical people (ie. my teachers) seem to think that 0.9999... is equal to 1, and I believe some exam papers (I've definitely tried some practice papers where this is the case) require that you will assume this in order to get the right answer to the question.

[zatoichi]

1 only equals 0.999rec if you assume 1/3 = 0.333rec.

But how then can you equally divide 1 by 3 AND 4? If you work in 1/3rds, sure, 1 does equally 0.999rec. But that is NOT an exact measurement. The increment is so slight that it cannot be exactly measured, as 1 is not equally divisible by 3, much like 10 isn't.

If you assume 1/4 of 1 is is 0.25 then 1 equals 1.

1 is 1, not 0.999rec. Saying that 1 = 0.999 is a contradiction in itself because they are two different numbers.

[mario114]

Basically, I think, everybody agrees 0.3333...=1/3, now multiply both sides by 3

1/3 x 3=1
0.3333... x 3=0.9999....

Therefore 0.9999...=1



Ah, I'm so clever


What 1/3 doesn't equal 0.3333, it's just easy and normall currect to assume it equals 0.3 reacoricing for an invinte times, but it real terms of mathmatics you can't put 1/3 as a unit ither wise 1 would have to equal 0.9999 reacuring. arrr i hate maths anyway.

[Zakatu]

the line of working that looks dodgy to me is.

9X = 9.999... - 0.999...

9*0.99999....rec does not equal 9.999.....rec

does it? to me it sounds wrong. Surely at the end you will get a small bit of difference. The only way this would be true is if you did 10*0.9999rec

Therefore, the step where you took away 0.999 to leave 9 is wrong. It would infact leave a tiny bit left. 0.0000001 or something.

therefore the whole rest of the proof does not work.

[The Peeps]

I'm not too good at the old mathematical equations but I worked this out...

3-2 = 1

[Josh64]

how the hell you came up with that i dont know, 1 is 1, its like saying, a person is a monkey. well its not but if someone says 1 then thats what it is. But then again i dont know that much about maths...

[Sarka]

This is wher emy confusion set in aswell Zakatu.

.99999rec x 9 = 8.999rec1

But .99999rec x 10 - .9999rec = 9

Very odd....

[/ nando /]

..I think there's several more possibilities than the 0.9999..= 1 thing (if I can remember correctly) because our maths teacher in my last year at school showed us stuff like that near the end of term with a few different numbers.. but the number's had to end with 9s or something..

[Zakatu]

ah, god.

I've had a rethink and it seems to be mathematically right. I can't seen any errors in the working.

I think where the error lies (and there has to be one) is in an assumption made.

It seems small but 0.99999rec * 10 perhaps does not equal exactly 9.999999 rec because you have shifted everything one place forward, so what ever "inaccuracy" there is at infinite places has now become 10* bigger.

so assuming that 9.99999rec is the same as 10*0.999999 might be the downfall behind this.

However, i'm not very good at proofs and am probably wrong, because to me it seems mathematically right.

I think to solve this perhaps its all about the nature of infinite and what a recurring number actually is...definitions.

because tbh, there isn't any REAL difference between 9.999999 rec and 10. nothing that you can right down is there? but we do know they are not the same.

[Raining_again]

it is way too early for things like this :P

dabookerman comes up with a simple theory so im going with that :grin:

[Supergrunch]

Dabookerman is wrong; it's not rounded, it simply is 1.

With each 9 added, it gets closer to 1. You have to stop writing it out somewhere, as it is recurring and you would run out of space. At the point where you stop writing, it isn't equal to 1, but taken as a whole, the number is.

And 0.333rec isn't an approximation of 1/3- try dividing 1 by 3 with long division and see what comes out. This means that this proof does work, and although I personally think it is the neatest, the others work too.

[Zakatu]

Dabookerman is wrong; it's not rounded, it simply is 1.


It isn't one, 0.9999 recurring is not 1. its the closest it can be without being one, but it isn't 1.

The proof makes out that it IS exactly one, i think the proof is wrong somewhere.

[dukkadukka]

:grin: you really are a funny old bunch on this forum

[RoadKill]

Well I'm not getting into it, it's almost bannable on Something Awful and there isn't any way I'm publicly flogging this dead horse again.

[dukkadukka]

good man, i'm going to keep on watching in awe at the strangeness of it all though.

[Hank Scorpio]

You are all wrong, Neo = the 1, nothing else.

[zatoichi]

If 0.999rec = 1, then 9.999rec must = 10.

So if you multiply 0.999rec by 10, you are actually multiplying it by 9.999rec again.

If you put that in a calculator, it comes up with 9.9999989.

That itself should disprove the theory that 0.999rec is 1.

[Raining_again]

why cant 1 = 1 and 0.99999 = 0.99999? everythin has to be so hard in life :hmm:

[Dieter]

Dabookerman is wrong; it's not rounded, it simply is 1.

With each 9 added, it gets closer to 1. You have to stop writing it out somewhere, as it is recurring and you would run out of space. At the point where you stop writing, it isn't equal to 1, but taken as a whole, the number is.


Running out of space? Stop writing somewhere?

Kind of contradicts the 'recurring' bit. :woops:

[Dr. Fluffles]

If 0.999rec = 1, then 9.999rec must = 10.

So if you multiply 0.999rec by 10, you are actually multiplying it by 9.999rec again.

If you put that in a calculator, it comes up with 9.9999989.

That itself should disprove the theory that 0.999rec is 1.
You can't use a calculator because it will round off the answer.

The reason you can't find anything wrong with those proofs is because they are right :heh:.

[Supergrunch]

You can't use a calculator because it will round off the answer.

The reason you can't find anything wrong with those proofs is beacause they are right :P.

Hear hear!

As I said before, I've had to do maths questions where the exam assumes that you know 0.999rec is 1.

[RoadKill]

Clearly base 10 isn't the holy grail of number systems despite it's apparent simplicity.

[Hal_9Million]

How many 9's are there after the decimal point? If there's a set amount, then all of his equations are wrong. For example:

Let X = 0.999

•
Then 10X = 9.99

Subtract X from each side to give us:
•
9X = 9.99 - X

but we know that X is 0.999, so:
•
9X = 9.99 - 0.999
or: •
9X = 8.991

Divide both sides by 9:
•
X = 0.999


However, the ... after every number suggests that the 9's go on into infinity. Then we get the problem of infinity. The problem is, you cannot enter an infinate number into an equation and get an exact answer, you can only make an estimate. Take pi for example. This is used to find the area of a circle. To use the full number, you wouldn't get the calculation done, because the decimal places go on for infinity. Scientist have tried to see how far they can go before it finally ends, unfortuneately it's a random pattern, so goes on forever. They've mangaed to get it to several million decimal places, and it just keeps going. So to make things easier we round the number up to 3.14. This way, a calculation can be done easily. However, you will never get the exact number you require. But to get it perfect does not concern us, as it's a waste of our time. To round something up or down, simplifies it to the point we need. The only people who need to be precise in these cases are people like NASA. They needed to get the calculations for the mirror in the Hubble space telescope accurate to millionths of a milimetre in order for it to work. We only need to calculate as far as we can see. So to get it more accurate than say several hundred atoms either way would be wasteful, as there's not much an atoms difference is going to make in comparrison to what our own eyes see. OK this my be confusing, but basically, you only need as many decimal points as necessary to your bounderies. If you're measuring the area of a circlular section of say a clock face, you aren't going to be more accurate than a milimetre at most, because it isn't necessary. So we come back to the statement of 1 = 0.99999999... No this is incorrect! 0.99999999... going on into infinity never ever reaches the exact value of 1. It get's extremely close however. So close, that it isn't any cause of our own concern. Therefore at this stage, you can round it up to the nearest whole number "1" and say that's it's 1. In actual fact it isn't, but you can say it's pretty damb close. It's so close in terms of human thinking, that it really doesn't matter. We don't need to know how many billions of 9's there are after the decimal point as that's close enough to 1 for us to just call it 1 for simplicity. It's still not 1, but it's really damb close. The connection cannot be proven with an equation, simple as that. X will always equal the same number. Otherwise, it isn't an equation. Equations are all about equality. if this guy put that crap down in an exam, he'd get a big fat 0 marks, because an equation must be equal on both sides, so the value of X cannot change. That is impossible! This guy is only 14, he's only been doing algebra for about year or two, so his knowledge is limited.

[tendosgirlfriend]

oh..my..god. :confused:

[Zakatu]

Good point Hal_9 million

I think we might need a maths graduate or something to give a definitive answer. I've just finished my a2, i know that his proof is not wrong in terms of the algebra. but i'm sure its wrong due to assumptions made about the recurring numbers and how to manipulate an infinite decimal place number, which is impossible surely.

[Dieter]

Plus this guy is only 14, just laugh at his infantile stupidity. Unless you yourself are also 14, or younger. Well I'm sorry if he's confused you. Tell him to talk to me, as I've just done an A-Level in Maths, so I could out-talk his misunderstood statements easyly.


And you'd think that elitism would be gone with post counts....

-edit-

Your post was perfectly fine until you started ragging on a guy that just asked a question. :hmm:

You obviously didn't A-level your elitist ass through English, did you?

[RoadKill]

If only his English was as good as his pathetic rants...

[Dr. Fluffles]

Plus this guy is only 14, just laugh at his infantile stupidity. Unless you yourself are also 14, or younger. Well I'm sorry if he's confused you. Tell him to talk to me, as I've just done an A-Level in Maths, so I could out-talk his misunderstood statements easyly.
Oh man, that post was hilariously funnny. Suffice it to say that you are indeed wrong. You haven't yet said why those proofs are wrong either. As I said, there is a reason for that...

[Supergrunch]

Well I did just write a long post pointing out the flaws in his argument, but IE crashed on me.

After changing to firefox...

My basic point was that the body of his post was both irrelevant and incorrect, and if 0.999rec wasn't equal to 1, then calculators and computers wouldn't work properly.

There was also no need for him to be so bilious.

[Hal_9Million]

And you'd think that elitism would be gone with post counts....

-edit-

Your post was perfectly fine until you started ragging on a guy that just asked a question. :hmm:

You obviously didn't A-level your elitist ass through English, did you?


Oh, I'm sorry that it didn't make any sense for you written in my pigeon English. I just wrote a crap load of stuff in a short space of time, I don't give a shit about how good the English is. No I didn't study English A-Level, I wasn't interested, simple as that. That doesn't make me illiterate when I need to write something properly, but literacy isn't a top priority on these boards is it? OK, so having a go at someone for being younger isn't fair, but it's so fucking obvious that someone at that age isn't going to have a complex knowledge of maths. That's year 9 for God's sake, they've only been doing algebra for about year. Plus I simply hate smart arsed little shits!

[dukkadukka]

Plus I simply hate smart arsed little shits!
i feel the same...

[Shorty]

Mathematically a Bee cannot fly. Thus the only true solution is:

Math = Wank.

[BGS]

As far as I can understand it it goes like this.
0.999... Is a number which never ends. People who say "0.999... is always a little bit less than one" are wrong because the number in fact never actually ends and they are just assuming it to finish somewhere down the line.
The number is the same as the number 1 because the nines go off in to infinity.

That's the explanation as I understand it that the mathematicians give. I guess it makes sense if you think about it.

EDIT: It'd be the same for any number really that had recurring nines at the end.

Eg: 7.99... = 8

[DiemetriX]

Hal_9million owns you all :)

[Supergrunch]

Mathematically a Bee cannot fly. Thus the only true solution is:

Math = Wank.

Only if you take it a bee as a lump of mass, rather than colection of muscles etc.

And to Hal_9Million, aren't you being "smart arsed" yourself trying to disprove what you don't understand?

[masaki86]

Maths is all about impossibilities and theoretical assumptions; most of which are used in equations and advanced maths.

Mechanics is a section which often falls into this ideology. When calculating the speed of an object on a surface, you are often required to class the surface as perfectly smooth, where by the friction=0. This is impossible in our world, as no such thing exists, but we still use it in maths.

The same can be said about the 0.9999999999999rec=1 idea. It is all based around the degree of accuracy the people are looking for, but theoretically, it does equal 1. The further you go to infinity, the smaller the difference becomes, and it gets to a point where the gap is so minute that there is no point in classing it as a different number.

However, if you are classing 1 as purely one, ie a whole point, then yes, 0.999....does not equal one, However, maths dictates that it does, due to the theoretical, and often philosophical assumptions.

[Zakatu]

As far as I can understand it it goes like this.
0.999... Is a number which never ends. People who say "0.999... is always a little bit less than one" are wrong because the number in fact never actually ends and they are just assuming it to finish somewhere down the line.
The number is the same as the number 1 because the nines go off in to infinity.

That's the explanation as I understand it that the mathematicians give. I guess it makes sense if you think about it.

EDIT: It'd be the same for any number really that had recurring nines at the end.

Eg: 7.99... = 8


no, no and no!

Look, if you draw a graph then 0.99999 recurring is an asymptote to the x=1 (whatever). It gets ever closer to 1 but Never, ever, ever will it equal 1.

So, this 0.99999 recurring = 1 stuff is just not true.

The problem is that the number X in the said equation is infitesimily smaller than 1. Rather than a quantifiable number.

Its something to do with the way maths works but i think the proof only works due to assumptions about infinite.

[Dieter]

Oh, I'm sorry that it didn't make any sense for you written in my pigeon English.

Actually it's pidgin, if I recall correctly ;)

Glad you edited your initial post though. And I really can't see him being 'smart assed' anywhere, but I won't deny I was :woops:

Hal_9million owns you all :)

Where the hell did that come from?

but it's so fucking obvious that someone at that age isn't going to have a complex knowledge of maths.

Hence why he asked the question? :hmm:

[KingJoe]

Good point Hal_9 million

I think we might need a maths graduate or something to give a definitive answer.

You rang?
Don't worry if you're totally confused by this, lots of people are (at least half of the people on my teacher training course got this 'wrong' and decided that 0.99... wasn't the same as 1).
0.999...=1 (the key to this is in the '...' part)
Most of my usual strategies for explaining this have been used. The main reason for not acceptoing it is that the 'infinity' that most people come across in maths (or their lives) is the POTENTIAL infinity (i.e. an infinity that comes from repeating a process forever) the infinity that we deal with here is an actual infinity (which is the headwrecking one).
For those of you familiar with 'sequences and series' at a level, try making the sequence of numbers that goes 0.9, 0.99, 0.999, 0.9999,... and find a value for the limi of the sequence (or the series 0.9+0.09+0.009+0.0009+...)
There is no approximation involved, by the way.
it is also true for any number with a finite decimal expansionr: 1.0000000...=0.9999999... and 2.63000000...=2.629999999....

It's to do with the density of the real numbers (guven any two distinct real numbers, there's another one between them- I'm not going into the proof of that one!).

Taking the potential infinity route, 1-0.9=0.1, 1-0.99=0.01, 1-0.999=0.001.
as we add more 9's, we get closer to 1. If we add an INFINITE number of 9's...
The point is that there is no LAST '9' in 0.999... so there is no difference between 1 and 0.999...

Also, someone mentioned this being a fault of the decimal system, but it isnt:
in binary 0.1111111...=1 in trinary 0.2222222...=1 etc

If anyone is really confused (and desperate to know the correct answer (or prove me wrong...) then feel free to PM me or write it on the thread (but it seems to be annoying enough people to get locked pretty soon...

Hope I was of Help.
Joe

edit: This guy is only 14, he's only been doing algebra for about year or two, so his knowledge is limited.

he's also entirely correct

[Dieter]

KingJoe confirmed my suspicions, and he seems legit to me, so I bow down to thee!

[EEVILMURRAY]

However, the ... after every number suggests that the 9's go on into infinity. Then we get the problem of infinity. The problem is, you cannot enter an infinate number into an equation and get an exact answer, you can only make an estimate. Take pi for example. This is used to find the area of a circle. To use the full number, you wouldn't get the calculation done, because the decimal places go on for infinity. Scientist have tried to see how far they can go before it finally ends, unfortuneately it's a random pattern, so goes on forever. They've mangaed to get it to several million decimal places, and it just keeps going. So to make things easier we round the number up to 3.14. This way, a calculation can be done easily. However, you will never get the exact number you require. But to get it perfect does not concern us, as it's a waste of our time. To round something up or down, simplifies it to the point we need. The only people who need to be precise in these cases are people like NASA. They needed to get the calculations for the mirror in the Hubble space telescope accurate to millionths of a milimetre in order for it to work. We only need to calculate as far as we can see. So to get it more accurate than say several hundred atoms either way would be wasteful, as there's not much an atoms difference is going to make in comparrison to what our own eyes see. OK this my be confusing, but basically, you only need as many decimal points as necessary to your bounderies. If you're measuring the area of a circlular section of say a clock face, you aren't going to be more accurate than a milimetre at most, because it isn't necessary. So we come back to the statement of 1 = 0.99999999... No this is incorrect! 0.99999999... going on into infinity never ever reaches the exact value of 1. It get's extremely close however. So close, that it isn't any cause of our own concern. Therefore at this stage, you can round it up to the nearest whole number "1" and say that's it's 1. In actual fact it isn't, but you can say it's pretty damb close. It's so close in terms of human thinking, that it really doesn't matter. We don't need to know how many billions of 9's there are after the decimal point as that's close enough to 1 for us to just call it 1 for simplicity. It's still not 1, but it's really damb close. The connection cannot be proven with an equation, simple as that. X will always equal the same number. Otherwise, it isn't an equation. Equations are all about equality. if this guy put that crap down in an exam, he'd get a big fat 0 marks, because an equation must be equal on both sides, so the value of X cannot change. That is impossible! This guy is only 14, he's only been doing algebra for about year or two, so his knowledge is limited.

http://img241.imageshack.us/img241/1492/bored7rb.jpg

[Shorty]

I can't believe I'm saying this on a primarily nintendo based internet forum, but you guys are a bunch of geeks.

[Dieter]

I can't believe I'm saying this on a primarily nintendo based internet forum, but you guys are a bunch of geeks.

Because maths is so much geekier than gaming, right? :P

What do you think a console does? ;)

[#1cubeplayer]

Argh, I'll be damned if I argue over this, but I just want to say that 0.9999rec technically isn't equal to 1 or anything else other than itself. If you say it is, you have rounded. Simple as that, no?

Now to do some real mathematics homework. *sigh*

EDIT: I didn't read the last page so I didn't know I was going against someone with a degree. I still believe that 0.9rec isn't 1 unless you round.

[zatoichi]

going by that theory, what is the exact measurement of a quarter of 1?

[BGS]

err, did you really ask that?
0.25
...duh.

[Supergrunch]

I've realised the problem with this thread. The people who are mathematically orientated know that 0.999rec = 1, and provide proofs to show this. The people who aren't mathematically orientated don't believe this is true, but won't accept mathematical proofs to the contary because they're not mathematically orientated.

It be a vicious circle I tell thee!

[kopo]

I don't have a degree in math but it is assumed by many scientists and mathemathicians (and me) that 0.999... =1.
The problem people have is the concept of infinity.
It never ends. Think of it as a HUGE number, so huge in fact, that it's impossible for sums and substractions to change it. For example infinity minus 99999 billionzillionkwadrillion is still infinity. I also believe that +infinity - infinity is impossible, because both are so big. I'm not sure of this, i simply forgot.

As for the the proof that 0.999... = 1 see above somewhere :smile:

[zatoichi]

so how can a quarter be 0.25, when a third is 0.333rec?

4 quarters at 0.25 = 1
3 thirds at 0.333rec = 0.999rec

And so why isn't 0.333rec 0.34? In which case 1.02 = 1 as well?

[kopo]

I don't see how you can conclude if 0.333rec = 0.34 that 1.02 = 1.

[zatoichi]

multiply the 0.34 by 3, as you would the 0.333rec. If they're the same number, that is.

[Dieter]

multiply the 0.34 by 3, as you would the 0.333rec. If they're the same number, that is.

kopo wasn't commenting on the 0.33rec (.333rec is incorrect seeing as you have to put the recurring bit twice before the 'rec' iirc :p ) being equal to .34, seeing as it is in fact so.

1 = 1.02 is however completely and utterly wrong :)

[zatoichi]

well then if it is in fact so, then why is 1.02 = 1 wrong? If 0.333rec and 0.34 are the same number, that's like saying 0.34 is a third of 1, which is wrong. It's a third of 1.02.

[Haver]

I wish KingJoe had taught me maths :(

[Supergrunch]

0.333rec and 0.34 aren't the same number, someone's got a bit confused. The only numbers that we're saying are the same are 0.999rec and 1. I can see why you thought 0.34, although your logic is slightly twisted. 0.999rec (or anything with .999rec on the end) is a special case, as the number infinitely progresses towards 1, and thus (brain-twisting bit) is 1.

[zatoichi]

Wait. You're right. 0.333rec would infinitely progress to 0.3333.....4.

[Supergrunch]

No, it doesn't. I can't exactly explain why because I'm not good enough at maths, but I'm sure someone else here can.

It's to do with the fact the the number is 3 rather than 9. 9 is only 1 away from 10, making it much closer to the rounded number, and when the 9's reccur, then it is what was the rounded number, which is no longer a rounded number.

I believe (although I may be wrong) that 0.33999rec is equivalent to 0.34.

[The3rdChildren]

Math... Make... Third Children... Brain... Die.

[Zakatu]

Hope I was of Help.
Joe

Yes, you were. It was a really helpfull explanation.

BUT, even though i'd like to think i'm mathematically orientated i don't really understand it. The sticking point is when you said that because there is no "last" 9 then there is no difference between that number and 1 itself.

Its that bit i don't really understand, what you seem to be saying is anything that gets closer and closer for infinite will be the same as what it is approaching.

This goes against what i've allways been taught..., that even if something goes on for infinite, it will still never get there. I'm trying to think of an analogy, but if you were constantly accelerating then you would eventually reach the speed of light, right? but according to physics this is impossible. So your saying that if you kept on accelerating for INFINITE you would be going the speed of light?

Maybee its a poor analogy.

[Supergrunch]

Actually, according to physics, you can reach the speed of light, but not surpass it.

Anyway, are you trying to think of something like the graph of root x- the gradient gets closer and closer to 0, but never actually reaches it?

This is a different case. If you don't that proof, then look at some of the earlier ones, such as the ones with thirds, or x=0.999rec etc.

[BGS]

Wait. You're right. 0.333rec would infinitely progress to 0.3333.....4.

Argh Zatoichi, please, stop. You don't have that good an understanding of maths so stop saying people are wrong with your flawed mathematics.

0.333... will NEVER "progress" to or equal "0.3333......4"

BUT.

If it were 0.333999... then THAT would equal 0.334

It's the nines at the end that are key.


EDIT: Stop thinking that the 0.999... reaches or 'progresses' to 1 or whatever the number is that has the 0.999... at the end. It doesn't. It just EQUALS that number. the 0.999... goes on INFINITELY. It's an actual infinite rather than a potential one.

[zatoichi]

BGS - 'progress' wasn't my word, I was just using terminology that had been previously used to describe what was going on by somebody else to put what I was saying into context, so if you want to flame someone for their choice of words, flame that person (although you shouldn't because only dickheads flame people.)

Also, when did I ever say anyone was wrong? I was just adding to the debate. If you can't handle that, then why do you return to the thread? You could have just as easily said, like others did, 'no, that's not right, because ..... and this is the right answer', but instead you come in mouthing off like a Hyeena with nothing useful to say that hasn't already been said before. Jeez.

I was also on course for an A at A-level maths, before I left for other things. Even if wasn't though, why should anybody have to be mathematically orientated to participate in a thread? This forum's for everyone mate, not just elitist bastards.

Supergrunch explained it all pretty well. All you did was make me laugh at you.







By the way.... 0.999rec = 0.999rec
1 = 1

;)

[Zakatu]

Actually, according to physics, you can reach the speed of light, but not surpass it.

Anyway, are you trying to think of something like the graph of root x- the gradient gets closer and closer to 0, but never actually reaches it?

This is a different case. If you don't that proof, then look at some of the earlier ones, such as the ones with thirds, or x=0.999rec etc.

sorry, but i thought it was only light that could travel at the speed of light.

*gets very muddled*.

I also just don't get why if something is 0.99999... for infinite, WHY that makes it equal to 1? to me thats an approximation. Sure, the difference between it and 1 is nigh on nothing, but there IS a difference. Therefore it is not one.

[Supergrunch]

Well... it should be possible to write down all numbers right? (to a degree- I'm kind of exluding irrational and complex numbers)

If so, then the difference between 0.999rec and 1 must be a number you can write down, but you can't, therefore the difference doesn't exist and 1 = 0.999rec.

This is a wordy version of a proof someone posted further up.

[KingJoe]

People generally aren't comfortable with infinity and the main reason is that their experiences of life don'e give them much to draw on in the form of analogy to draw on.

You can write complex numbers down (3+2i, anyone) and irrational numbers too (sqrt(2)). The point is that there is NO number between 0.9999... amd 1. They are the same number. 0.99... isn't someone beginning with 0.9 and writing forever. Most of you agree that the limit as we keep adding nines gets closer to 1. In more precise terms, if we are given a number (no matter how small) we can find some number of 9's in our expansion so that the difference between our expansion and 1 is smaller than that number (ie, if we wanted to make the difference smaller than 0.000000000002, we simply have 11 9's or more) we simply have more 9's than the number of 0's in the decimal expansion.
Bear with me!
Ok, so by adding more an more 9'm makes the difference smaller and smaller.
so it makes the numbers closer and closer.
0.99... is itself a LIMIT. it is the limiting value of a sequence of more and more 9's. It is the value that adding more 9's gets closer to, because we are adding more 9's than have ever been concieved.
INFINTY ISN'T JUST THE BIGGEST THING YOU CAN THINK OF. IT'S MUCH BIGGER.
more 9's: closer to 1. An infinite number of 9's: infinitely close. Infinitely close : in the same place.

This is a bit of a crude argument but if you haven't got it yet than I can't think of a way to explain it to you. If 2/3rds of the potential maths teachers on my course couldn't get it then there's not a huge shame in it. If anyone is interested in finding a bit more out about infinity then hava a look here http://math.youngzones.org/Hotel_Infinity.html or google a man called Gregor Cantor.

edit: to whover wished I was their maths teacher, cheers!

[Zakatu]

Ok, i understood the word explanation(s). Just made me click.

Thanks.

leaves me feeling a bit unsatisfied, meh. it doesn't seem right, perhaps because nothing really is infinite.

[Mr_Odwin]

The point is that there is NO number between 0.9999... amd 1.

I think that this is the most important bit Zakatu. There are an infinite number of numbers so whenever you pick two of them you can always always always pick out a number that is between them. However, in the case that we are looking at you can't, therefore they are the same number.

[Zakatu]

yer, i understand.

I just think it was all a bit misleading to begin with, stating x=0.999...

when that is the same as one, may aswell of just said x = 1.

None of the manipulation was neccessary at all (multiplying it by 10?) it was misleading. because nothing was changed.

SHould of said what it was REALLY about from the start, i.e a recurring number is the same as the whole number it is near, as long as the recurring number goes on for infinite.

[Supergrunch]

When I said you can't write complex numbers or irrationals, I meant that you couldn't write them out in full- i is simply a representation and irrationals vary forever. I suppose you could say that 0.999rec is a representation, but people can realistically see from it exactly what the number implies, to however many decimal places they want.