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☖ Forums → Discussion Forum → Does 0.999 repeating equal 1?
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Does 0.999 repeating equal 1?
2007-03-10, 10:46 AM #121
Because you're adding a quantity to infinity in which case it's still infinity, regardless?

0.(9) = 0.9(9) = 0.99(9) = 0.9(99)

It's all infinity nines, no matter how you look at it.
2007-03-10, 10:53 AM #122
Freelancer - no.

If you don`t believe me, just take several series, which converge to infinity, and divide them in two. You`ll notice, that not every one will still converge to Infinity.


Monty - no. 0.99(9) != 0.99(99)
As to why, enquire into series. You`ll see, that those series are represented differently. They both converge to 1, but they are NOT the same.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 10:55 AM #123
Go jump off a cliff. Seriously. You'd raise the world's average IQ by a couple points.
"it is time to get a credit card to complete my financial independance" — Tibby, Aug. 2009
2007-03-10, 11:07 AM #124
Are not ad hominem attacks a first sign of losing an argument? ^_^

Just admit that I`m right, and we can save you much embarassment later.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 11:21 AM #125
Why would anybody that knows you're wrong admit that you're right? You shot your intellectual credibility in the foot in the comma thread.

The problem is that we can't prove you wrong because you are demonstrating gross misunderstanding of fundamental mathematical principles.
Detty. Professional Expert.
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2007-03-10, 11:29 AM #126
Sorry I wasn't here to back you up earlier, Freelancer; I like to sleep in on saturdays :P

Okay there seems to be a lot of misinformation in this thread. Since I have seen several proofs that 0.99... and 1 are equal, and thus mathematics at some level is completely broken if they aren't, I'd like to issue this challenge to those who believe it is not:

It is an intrinsic property of the real numbers that for any two distinct points on the number line, one can always find another point between them. This is part of the very definition of the reals and therefore no semantic wrangling can get around this fact. So, knowing this, and assuming that 0.99... and 1 are not the same number (i.e. not equal), you should be able to describe, mathematically or just in plain English, a number that is between the two. If you can find a number that is between 0.99... and 1, I will recant my previous stance and admit that I was wrong.
Stuff
2007-03-10, 11:38 AM #127
Number between 0.9(9) and 1?

Easy -> 0.99(9)
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 11:40 AM #128
Wait wait wait. Did you seriously just put another 9 onto the end of an infinite string of nines?

Do you know what "infinite" means?
Stuff
2007-03-10, 11:45 AM #129
That`s exactly it. There is ALWAYS one more nine, no matter how many there are. THAT is what infinity is. And for every nine in the row, there is ALWAYS next one, and result will be inbetween of previous one, and 1.

It`s impossible to treat infinity as a finite number, as all of you attempt to.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 11:50 AM #130
Not a single person who answered 'no' has ever even taken precalc.

Everybody who answered 'yes' is a cool dude like me. :cool:

Edit: JG I'm disappointed in you I expected better. :argh:
2007-03-10, 11:53 AM #131
Originally posted by Alice Shade:
That`s exactly it. There is ALWAYS one more nine, no matter how many there are.
here's what he's asking: what is the difference between 0.9999... and 1?

Think about this.

What's the difference between 1 and 2?
What's the difference between 1 and 1?
What's the difference between 1.00000... and 1?
What's the difference between 0.99999... and 1?

How much would you have to subtract from 1 to get 1?
How much would you have to subtract from 1 to get 0.99999...?
2007-03-10, 11:55 AM #132
Just from a limit point of view .9 repeating approaches one, I guess.
Steal my dreams and sell them back to me.....
2007-03-10, 11:59 AM #133
I already answered that.

You subtract 0.0(0)1 from 1 to receive 0.9(9).

Or, 1/inf, if that`s more suitable for you. Proverbial infinitesmall value, that is closer to zero, then anything - yet not zero.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 12:04 PM #134
[quote=Cool Matty]
And of course you can say "no matter how much of infinity of nines you put, there's always room for more". Which is exactly why you can't state 0.0...1. The 1 might as well not exist because no matter how you look at it, you will never reach that one. EVER.[/quote]

(!!!)
幻術
2007-03-10, 12:05 PM #135
Oooo. Oooo.

I know the answer.

It doesn't matter, there's no practical reason to answer this question.
"If you watch television news, you will know less about the world than if you just drink gin straight out of the bottle."
--Garrison Keillor
2007-03-10, 12:05 PM #136
Didn't I just say that if two numbers aren't equal then there must be a number between them?

If your "proverbial infinitesimal value" is not zero, as you say, then it can't also be "closer to zero than anything". There is no number that is closer to zero than any other number.

If you disagree with this then we aren't even using the same number systems, and thus argument is impossible.
Stuff
2007-03-10, 12:10 PM #137
Again I say:

In the set of real numbers that are no nonzero infinitesimal numbers.

Fetched directly from the "Infinitesimal" article on Wikipedia.
Detty. Professional Expert.
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2007-03-10, 12:11 PM #138
Hah, not so fast.

Infinitesmall value is NOT a certain number. It`s an abstract concept of what would 1/inf equal. It can`t be zero - no matter, how small are the parts you break something on, parts don`t just disappear, when they are small enough.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 12:21 PM #139
Quote:
In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. A number x is an infinitesimal if and only if for every integer n, |nx| is less than 1, no matter how large n is. In that case, 1/x is larger in absolute value than any positive real number.

Nonzero infinitesimals are not members of the set of real numbers.


This makes it very clear that for a real number to be infinitesimal it must be zero.

I don't know how this can be made any clearer. Even a mentally retarded person could understand it based on this fact.
Detty. Professional Expert.
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2007-03-10, 12:28 PM #140
Gah, NOT!

If infinitesmalls were all ZERO, why would there even be all the bother with infinitesmall values in first place?!

People`d just name them ZERO, and be done with it.


Also, I notice a curious thread. Why do you try to apply REAL NUMBERS to infinite series?
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 12:47 PM #141
^^ I remember doing some proofs with series even infinite series and I had to mark forall n in R.

Originally posted by Jon`C:
Not a single person who answered 'no' has ever even taken precalc.

Everybody who answered 'yes' is a cool dude like me. :cool:

Edit: JG I'm disappointed in you I expected better. :argh:

Yeah I'm kind of ashamed. I've had calc up to discrete maths. I should know better! :saddowns:
Code to the left of him, code to the right of him, code in front of him compil'd and thundered. Programm'd at with shot and $SHELL. Boldly he typed and well. Into the jaws of C. Into the mouth of PERL. Debug'd the 0x258.
2007-03-10, 12:53 PM #142
1/9 = 0.1111111...
5/9 = 0.5555555...
8/9 = 0.8888888...
9/9 = 0.9999999... and we all know 9/9 = 1

Try taking a calculus class if you wonder about such things.
This is retarded, and I mean drooling at the mouth
2007-03-10, 12:57 PM #143
Um. You realise, that they are NOT strictly equal in any of those equations?
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 2:59 PM #144
After my short unsuccessful venture into this thread I realised something:
http://xkcd.com/c230.html
Sorry for the lousy German
2007-03-10, 3:51 PM #145
I assure you, that whilst I find these discussions interesting, i'm only taking part because I have nothing better to be doing.
Detty. Professional Expert.
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2007-03-10, 3:59 PM #146
Isn`t it the only valid reason to do so? I don`t think that Earth will rock off the orbit, no matter what the conclusion here will be.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 4:17 PM #147
True; despite how well calculus works in describing physical events, the universe is perfectly happy being quantized. :P

In fact if it weren't, it would lend it self to all sorts of silly little things like the Banach-Tarski Paradox
Stuff
2007-03-10, 4:26 PM #148
Heh. Well, yes. Pure mathematic is rather disconnected from physical realities.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 6:08 PM #149
Rrragh

Same thing I posted last time.
Attachment: 15662/series1.jpg (8,437 bytes)
一个大西瓜
2007-03-10, 6:14 PM #150
I didn't read all three pages of comments on such a simple question.

I also have no idea how to explain myself.

If A = 0.999... and B = 1

Then. um... A does not equal B.

And if you respond to this and show me an error in my logic, I will not care. Maybe there is an error in my math, again, I will not care. In my opinion, they are not the same.
2007-03-10, 6:17 PM #151
Originally posted by Axis:
And if you respond to this and show me an error in my logic, I will not care. Maybe there is an error in my math, again, I will not care. In my opinion, they are not the same.


Wait, so math is about opinions now and not logic?

There aren't enough psyducks in the world. But here, I'll start with this one. :psyduck:
Stuff
2007-03-10, 6:22 PM #152
Originally posted by Alice Shade:
Now, this is more like it.

Let`s take 0.9(9) as an infinite series.

A1=0.9, An=An-1/10

Now, obviously, series CONVERGE to 1. It means, that they are forever approaching it, but do not become it.


I don't know what you're talking about. What is "they"? The successive terms int the series? Obviously they don't, but the definition of a series is a sum. The definition of the value to which the series converges IS the value of that series's sum. Maybe you were thinking of sequences?
一个大西瓜
2007-03-10, 6:22 PM #153
He's saying that simply because 1 and 0.999... don't look the same then they're not. However applying that logic 1 != 1.00.
/fluffle
2007-03-10, 6:27 PM #154
Originally posted by kyle90:
Wait, so math is about opinions now and not logic?

There aren't enough psyducks in the world. But here, I'll start with this one. :psyduck:


I don't know. The main thing is, I don't care. :downs:
2007-03-10, 6:27 PM #155
I used they to refer to "series" automatically, because it looks like plural form.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 6:29 PM #156
Originally posted by Detty:
No.

Because I still know that 0.9... equals 1.

First let's look at infinite series. If a series converges to 1, it means that should we reach the infinite(th?) entry in the series the value will be exactly 1.

0.9... is not saying "here is an infinite series," it's saying "here is the result of the infiniteth value in the series". 0.9... is not a process it's the result and it equals 1.

Secondly, let's not get smart and go on about other numerical systems. In the standard set of real numbers, there are no nonzero infinitesimal values that are members of set. This means that your precious- infinitesimal-difference-is-still-a-difference argument is using a difference of 0. Now, if the difference between 0.9... and 1 is 0, wouldn't that make them equal?

There are so many different proofs that 0.9... equals 1, just pick one that you like the best.


wow, detty got it spot on here.
2007-03-10, 6:35 PM #157
Originally posted by Darth_Alran:
no, if .9999999... truly is .9999999.... then it does not = 1... it is .9999999... unless you add .1111111... or unless your not dealing with absolutes.



actually u add .0000001 to get 1, not .1111111, or u will get 1.111111
Matt
2007-03-10, 6:36 PM #158
Originally posted by Alice Shade:
I used they to refer to "series" automatically, because it looks like plural form.


(Series can be singular, though.)

Anyways, my point is that because the value to which a series converges IS the sum of that series, the proof I posted above shows pretty obviously that the series in question has a sum of 1.

(The concept of having a finite sum to an infinite series isn't anything special. Gabriel's Horn, for example, has infinite length and surface area (hence an infinite number of circular "slices") but finite volume.)
[Edit: I just realized how stupid the paragraph above is because it's so blatantly obvious. INTEGRALS! Finite sum of an infinite number of things!]

In any case, here's a Wikipedia page containing a crapload of proofs (including the one that I did above) concerning the issue:

http://en.wikipedia.org/wiki/0.999...

Incidentally, the proof I did was published by Euler in his Elements of Algebra, which I did not know.
一个大西瓜
2007-03-10, 9:02 PM #159
I've never taken precalc (unless trig counts :downs:) and I still know for a fact that 0.999... = 1

So far this "Alice Shade" guy (Who keeps calling me Monty for some very odd and annoying reason) hasn't provided a single shred of evidence that he has any understand of basic concepts of algebra, much less calc.
2007-03-10, 9:35 PM #160
Originally posted by Alice Shade:
Are not ad hominem attacks a first sign of losing an argument? ^_^

Just admit that I`m right, and we can save you much embarassment later.


No, the ad hominems are flowing because trying to convince you of mathematical FACTS is like pulling my own teeth out one by one with a rusty pair of pliars.
"it is time to get a credit card to complete my financial independance" — Tibby, Aug. 2009
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