NationStates Jolt Archive

Proof:

lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1
0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

Discuss.

how many more people are going to feel the need to prove this here? I swear there's like one a week, and it's not even like the endless "Bush is teh evil" or "teh war is teh evil" or "god is teh evil" threads, because these are always identical.

Tribes R t3h spellxorz

0.999...=1 as a consequence of the definition of decimal expansion. Unfortunately the definition is only usually taught at university, so almost all people that use decimal numbers don't truly understand them.

that was already rather non-thrilling when my extremely hot math teacher ran me through it three years ago, so..

[and this has been on here before? in the math puzzles thread maybe? must have missed it.]

that was already rather non-thrilling when my extremely hot math teacher ran me through it three years ago, so..

[and this has been on here before? in the math puzzles thread maybe? must have missed it.]

Yes, it's in there. It's had its own thread before, too. I could go dig some up, but I'm really lazy.

I'm adding this to my list of pseudo-intelligent newbie threads, along with Dihydrogen Monoxide and Science can't prove shit. And that is how 'prove' is spelt, regardless of what certain warriors may think :p

No...oh dear GOD NO!

I. Hate. MATH!

GAH!

*dies*

I'm adding this to my list of pseudo-intelligent newbie threads, along with Dihydrogen Monoxide and Science can't prove shit. And that is how 'prove' is spelt, regardless of what certain warriors may think :p
Psuedo-intelligence?

Wrf?


Only idiots do not think that .999~!=1

my son once told me that if i wanted to start a thread that would not only get tons of posts but was also guaranteed to degenerate into a spectacular flame war, this was the one to start

i considered it but i just couldnt bring myself to give a damn about the question.

It is not clever to 'prove that 0.999 equals 1', 'that 0.999 does not equal 1', or 'that 0.999 equals abortion is murder'. It's really not. Try some real maths.

It is not clever to 'prove that 0.999 equals 1', 'that 0.999 does not equal 1', or 'that 0.999 equals abortion is murder'. It's really not. Try some real maths.
Why don't you try not be idiot kthnx. Learn math .999~=1

I'm adding this to my list of pseudo-intelligent newbie threads, along with Dihydrogen Monoxide and Science can't prove shit. And that is how 'prove' is spelt, regardless of what certain warriors may think :p

crap

crap
then u r not a smrt person. vcause dihydrogenmonoxide is vry dangerous and .99~=1

then u r not a smrt person. vcause dihydrogenmonoxide is vry dangerous and .99~=1

Just because I made an error on prove doesn't mean I'm not going to flame your arse if you keep talking to me like that

Psuedo-intelligence?

Wrf?


Only idiots do not think that .999~!=1
No. Pseudo-intelligence as in you could have just ctrl+c ctrl+v'd this directly from another thread/forum/website/whatever and passed it off as 'OMG I jsut liek well lernt this in maffs lololololololol I r teh gr8'. I'm not suggesting you did this - well actually I am, and if you show us otherwise then I'll give a full apology - I'm just saying, and hear me clearly; IT'S BEEN DONE.

EDIT: Also - Wrf? Do we have dogs using the forum now?

This thread has the potential of becoming a great glob of trash.

This thread has the potential of becoming a great glob of trash.

potential to become?

So, how about that Riemann hypothesis?

All I know about that is it's not been proved. I don't profess to understand what it actually means, though: little beyond my level, I'm afraid.

Sweet! I remember doing problems like that last year in Algebra 2!!!

All I know about that is it's not been proved. I don't profess to understand what it actually means, though: little beyond my level, I'm afraid.

It's got some fascinating links to quantum theory; I believe that at least one mathematician is using quantum theory to attempt to prove it. Very complex; I can only superficially understand it. Perhaps once I get my degree...

So, how about that Riemann hypothesis?
The Riemann hypothesis is great - if true, it means that the distribution of prime numbers differs from the standard expression approximating the distribution by the distribution representing the sum of random equiprobable events. Did that make any sense? Well, it's profound anyway.

The Riemann hypothesis is great - if true, it means that the distribution of prime numbers differs from the standard expression approximating the distribution by the distribution representing the sum of random equiprobable events. Did that make any sense? Well, it's profound anyway.

It did, to an extent. Unfortunately, I only have a 12th grade knowledge of calculus (at least until I get to Ohio State, where I'm going to major in mathematics) and have only been able to supplement my knowledge to a certain degree.

The Riemann hypothesis is great - if true, it means that the distribution of prime numbers differs from the standard expression approximating the distribution by the distribution representing the sum of random equiprobable events. Did that make any sense? Well, it's profound anyway.

I think I followed that, but why is it profound?

And is there any reason I should care that 0.999(r)=1?

And is there any reason I should care that 0.999(r)=1?

No, it's just mildly interesting.

I don't think it does...

if 0.999(r) has an infinite number of 9s following the decimal point, then multiplying it by 10 means that it now is 9 followed by an infinite number of 9s, minus 1.

Now, you subtract the original X, which was 0.999(r). However, this has an infinite number of 9s following the decimal whereas the 9.999(r) has an infinite number minus one.

This means, if infinity could be quantified, it would look something like this, where the number following the (r) is the true end of the number:

x = 0.999(r)999
10x = 9.999(r)99
9x = 8.999(r)991
x = 0.999(r)999

The simple problem comes in that you cannot quantify an infinite.

I don't think it does...

if 0.999(r) has an infinite number of 9s following the decimal point, then multiplying it by 10 means that it now is 9 followed by an infinite number of 9s, minus 1.


infinity minus one is infinity, I believe. Because it's infinite. Weird concept, but there it is.

It did, to an extent. Unfortunately, I only have a 12th grade knowledge of calculus (at least until I get to Ohio State, where I'm going to major in mathematics) and have only been able to supplement my knowledge to a certain degree.
Here's a not-too-tricky page on the subject, and if you get bored of all the maths then there's a nice animation demonstrating what it's all about a little below the middle of the page:

http://www.maths.ex.ac.uk/~mwatkins/zeta/encoding1.htm

I don't think it does...
The simple problem comes in that you cannot quantify an infinite.

You have to look at it as a fraction.
1/9=.111111111....

1/9 times 9 is equal to 9/9, or 1. However, .1111111 times 9 is also .9999999 repeating, and so .9999999=9/9=1.

You can also see it with 1/3; 1/3 is .3333333..., but 3/3 is one and .3333333 times 3 is .99999999

infinity minus one is infinity, I believe. Because it's infinite. Weird concept, but there it is.
Infinity isn't a number (in the traditional sense). The best you can say here is that if you remove one object from a infinite series of that object, you still have an infinte series of that object.

You have to look at it as a fraction.
1/9=.111111111....

1/9 times 9 is equal to 9/9, or 1. However, .1111111 times 9 is also .9999999 repeating, and so .9999999=9/9=1.

You can also see it with 1/3; 1/3 is .3333333..., but 3/3 is one and .3333333 times 3 is .99999999

Aye, I caught that. It's an interesting anomaly in math.

Here's a not-too-tricky page on the subject, and if you get bored of all the maths then there's a nice animation demonstrating what it's all about a little below the middle of the page:

http://www.maths.ex.ac.uk/~mwatkins/zeta/encoding1.htm

Thanks. It's quite interesting reading. :cool:

Infinity isn't a number (in the traditional sense). The best you can say here is that if you remove one object from a infinite series of that object, you still have an infinte series of that object.

Weird shit like that is why I gave up Maths after A-Level. Thanks, though for the fucking headache **grin**

Aye, I caught that. It's an interesting anomaly in math.
There's nothing wrong with mathematics, it's just that few people understand what a decimal expansion actually *means* ('cause it's not taught until univeristy), and hence come up with nonsensical logic like that you quoted.

I don't see why people make such a fuss about the .9 equation. I mean, it's 1-(1/i), since 1/i is obviously smaller than any finite number to the right of the 0 point, there's no surprise .9~ equals 1. I guess people go all "OMG there's a 1 after the infinite amount of zeroes, it must be less than 1!" but that's really just a misconception stemming from inadequate knowledge of the concept of infinity.

Besides, there is a rule for converting to decimals: for a.bcdcdcd~ with cd repeating, a.bcd~=abcd-ab/[number of nines equal to number of repeating numbers, number of zeroes equal to non-repeating numbers after decimal point].

Thus, 0.9~=9/9=1. It's not so much a wonderful exception to the rule which allows you to end the cruel dominion of math over common man as it is part of the definition.

Aye, I caught that. It's an interesting anomaly in math.It is not an anomaly. It just looks wierd.

And I think I started this thread once. Maybe it wasn't me, but I spent a lot of time with it. I'm with whoever it was above that suggested that those who don't "believe" that .999r = 1 fail to understand the concept of infinity. They tend to bring up what is at the end of the nines. There is no end! The only problem I have with infinity is grasping the concept of multiple levels of infinity, which is suposedly a valid concept.

BTW, when you non-Americans say 'maths', you sound retarded to us (well, to me anyway). Do we sound retarded to you when we say 'math'?

If you owe me a dollar, I don't want to be paid back in 99.999~ cents, I want $1, in bill form, because having that many pennies is such a pain. Which brings me to the truly confounding math that comes into economics, where my $1 isn't actually $1, but really has some absurd value that we ignore.

If you owe me a dollar, I don't want to be paid back in 99.999~ cents, I want $1, in bill form, because having that many pennies is such a pain. Which brings me to the truly confounding math that comes into economics, where my $1 isn't actually $1, but really has some absurd value that we ignore.

What?

If you owe me a dollar, I don't want to be paid back in 99.999~ cents, I want $1, in bill form, because having that many pennies is such a pain. Which brings me to the truly confounding math that comes into economics, where my $1 isn't actually $1, but really has some absurd value that we ignore.

Is it really called "piece of eight" because they used to cut the coin in eight?

If you owe me a dollar, I don't want to be paid back in 99.999~ cents, I want $1, in bill form, because having that many pennies is such a pain. Which brings me to the truly confounding math that comes into economics, where my $1 isn't actually $1, but really has some absurd value that we ignore.
If economists are telling you that, you can safely ignore them.

And since I don't owe you a dollar, you're point is pointless.

If economists are telling you that, you can safely ignore them.

And since I don't owe you a dollar, you're point is pointless.

Actually, his whole argument is quite faulty: The 99.9~ cents cannot be intended to be paid in cash, since there's no 0.9~ cent coin or any currency. That leaves us with electronical means, in which case the computer will equalize those 99.9~ to 1.

BTW, when you non-Americans say 'maths', you sound retarded to us (well, to me anyway). Do we sound retarded to you when we say 'math'?
Yes, especially when you say 'math'. I thought using British spellings was meant to command respect (as long as the person doing it isn't American) - that's what Americans have told me before.

Yes, especially when you say 'math'. I thought using British spellings was meant to command respect (as long as the person doing it isn't American) - that's what Americans have told me before.

Isn't it called "the science of mathematics"? That makes "maths" sound sensible enough to me, though apparently people really get annoyed by it.

Speaking of which, why is it plural?

Isn't it called "the science of mathematics"? That makes "maths" sound sensible enough to me, though apparently people really get annoyed by it.

Speaking of which, why is it plural?
Ending with an 's' does not make a word plural. Observe that 'mathematics' is used with a singular verb - for example, 'mathematics is/*are interesting'.

Ending with an 's' does not make a word plural. Observe that 'mathematics' is used with a singular verb - for example, 'mathematics is/*are interesting'.

Yes, but with an s after a consonant a person with a less than perfect grasp of English is inclined to assume it is plural. As far as I know there are only a handful of similar exceptions to the pluralization rule, and the only one I can remember is mathematics.

EDIT: Oh, hang on, nevermind. I figured someone probably dropped the "o" in "mathematikos". Makes sense, little as it may be.

Yes, but with an s after a consonant a person with a less than perfect grasp of English is inclined to assume it is plural.
English grammar has thousands of bizarre exceptions - consistency would imply we should fix them all if we fix any, and I doubt many English speakers/writers would be receptive to such a move.

English grammar has thousands of bizarre exceptions - consistency would imply we should fix them all if we fix any, and I doubt many English speakers/writers would be receptive to such a move.

Seems to me I got an e-mail about that one time... I'll go look for it.

Found it.

"The European Commission has just announced an agreement whereby English will be the official language of the EU rather than German, which was the other possibility. As part of the negotiations, Her Majesty's Government conceded that English spelling had some room for improvement and has accepted a 5 year phase-in plan that would be known as "EuroEnglish": --

In the first year, "s" will replace the soft "c". Sertainly, this will make the sivil sevants jump with joy. The hard "c" will be dropped in favor of the "k". This should klear up konfusion and keyboards kan have one less letter.

There will be growing publik enthusiasm in the sekond year, when the troublesome "ph" will be replaced with the "f". This will make words like "fotograf" 20% shorter.

In the 3rd year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible. Governments will enkorage the removal of double letters, which have always ben a deterent to akurate speling. Also, al wil agre that the horible mes of the silent "e"'s in the language is disgraceful, and they should go away.

By the 4th yar, peopl wil be reseptiv to steps such as replasing "th" with "z" and "w" with "v".
During ze fifz year, ze unesesary "o" kan be dropd from vords kontaning "ou" and similar changes vud of kors be aplid to ozer kombinations of leters.

After zis fifz yer, ve vil hav a reli sensibl riten styl. Zer vil be no mor trubls or difikultis and evrivun vil find it ezi tu understand ech ozer.

ZE DREM VIL FINALI KUM TRU!!

EDIT: Quote tags own me.

I think you should tell the guy to add "q" in there somehow.

Seems to me I got an e-mail about that one time... I'll go look for it.

Found it.
Note that it continues to use 'ch' after the letter 'c' has been abolished (sorry to complain about the joke, but I've seen it so many times now). Of course 'ch' could be replaced with 'tsh', as they're the same sound.

Note that it continues to use 'ch' after the letter 'c' has been abolished (sorry to complain about the joke, but I've seen it so many times now). Of course 'ch' could be replaced with 'tsh', as they're the same sound.

Hot damn. You're right. Wish I knew where this thing originated, I'd send your criticism along.