omg new proof

Assumptions
If A = B, then
a)  A-B = 0
b) A = (A+B)/2 = B

If A > B, then
a)  A-B > 0
b) A > (A+B)/2 > B


Let A = 1, B = .999...9
a) A-B = 1-.999...9 = .000...1 =/= 0
b) (A+B)/2 = (1+.999...9)/2 = 1.999...9/2 = 1.999...95 < A

Therefore, .999...9 =/= 1

>>39
Euler is dead. Good luck telling him something.

ITT freshmen/dropouts saying PhDs are wrong, without even understanding the arguments.

Brilliance.

>>35
Was all that neccassary to establish that x=1?
You could just say, x=1. And the rest of your statement is dumb too.

>>38
I did provide what you asked for, in >>25. 0.999... is equal to 1, and 1 is a real number. If you knew the definition of the real numbers as limits of cauchy sequences of rationals you'd know this already, but you don't, so you must not have taken analysis, because this is taught in every introductory analysis class everywhere. QED. Furthermore, you can't even find the limit of a geometric series (>>26), and since limits of geometric series are taught in high school calculus or earlier, you must not have taken high school calculus.

>>39
Euler worked with (traditionally) non-convergent series not using standard summations, but instead using things like Abel summations.

>>38
Wrong again.

0.9... is NOT a number. Sure, 0.9 is a real number, so is 0.99, 0.999, etc; but no matter the number of 9s there are in the number you pick, at least one will always be missing. An element that is not in R cannot equal an element that is in R.

So drill it into your stupid fucking head: The real numbers are an infinite set of FINITE numbers; not an set infinite set of infinite numbers.

>>45
1 = 0.999...
Also, by your definition, the real numbers would be countable, pi would not be a real number, and the "set" of real numbers would be a different set* based on what base you choose! Talk about stupid.

* - by your definition, 1/3 is not a real number, since its decimal expansion, 0.333..., is infinite. But in base 3, 0.1 represents 1/3. Whoops!

>>45
Also, I forgot to mention, you just replied telling someone they were wrong and then agreeing with them. Good job.

>>46
Of course 0.333... is not a real number, but 1/3 in base 3 is a real number because you can find a finite base in which it can be finitely represented. If you have a set S = {a, b, c} and a set T = {a, b, d}, you cannot say that any element in S v T, but not in S ^ T, has a corresponding element in the other set. Simple. Same principle here.

Let A = .999~
Let B = 1
.999+1/0 = conspiracy

>>48
Countable, Pi is not a real number. You have two problems to deal with still, and you've basically just accepted the fact that your definition of the real numbers can not be represented in one base, contrary to the "actual" real numbers (you know, the set that every mathematician in the world is familiar with and agrees upon). Furthermore, your definition offers no advantages over the "actual" real numbers to make up for this deficiency. As you've stated it in this most recent post, the real numbers are the rational numbers.

>>50
Well, you also have the irrational "numbers". They are locked away in a mental hospital until they can accept the fact that they are not real.

>>51
Yes, I do have the irrational numbers. You, however, don't.

>>51
You stupid shit they are too real.

>>53
>>51 can't handle irrational numbers because they're _too real_.

>>54
Pi is a li!

>>52
>>53
>>54
You are all in denial of a truth you can't handle.

>>38
1
that is a real number that exactly represents .9 repeating

sum(n=1, +inf)[(9)10^-n]

Work with the equation a bit and you will see.

>>38

The problem is that you stated something that was blatantly false to anyone who understood the math you were talking about.  Go back and look at >>20.  ZOMG, sum(n=1, +inf)[(9)10^-n] = 1.

>>57
>>58

God damn why do the text boards only show the first fucking 40 replies

>>48
>Of course 0.333... is not a real number,


OH LAWDY I LOL'D

>>50

Pi is real you nigger.  It's irrational, but real.

>>58
>>59
>>60
>>61

oh god when did this ID thing show up lollerskates

fail equation is fail.
op assumes 0.99999.... =/= 1 threfore it doesn't.
if he assumes 0.999999.... = 1 then his equation proves 0.9r = 1.
fuckwit

You are all brainwashed phailures. See what happens when you don't think for yourself?

>>61
Moron, I was pointing out problems in the other morons definition of the real numbers. Read the whole post before commenting.

>>64
Jesus, did I make a wrong turn and end up on sci.math? I haven't seen a crank/troll this bland and lazy since the mid-90's.

>>65
There is no problem in my definitions. Many mathematicians often get very homicidal/suicidal when they are proven wrong about something "big". This happens every once in awhile.

If you want to change the current definition of 'real number,' you kinda have to have a pretty good reason. You know, one other than 'I wanna feel smrt.'

>>66
Your "definition" of the real numbers makes the real numbers and the rational numbers the same thing. Why even bother?

Furthermore, there's nothing "proven wrong" at all by a definition switch, even if I was willing to accept it. To prove anyone wrong you have to use the same definition and (gasp) PROVE them wrong. For example, if I say "every natural number is even", and you respond that 1 is not even, and I reply that the natural numbers are the set {0, 2, 4, 6, ... }, did I just prove you wrong? Of course not, because I changed a definition that is UNIVERSALLY ACCEPTED to make my argument, and even if you were to allow my new definition I haven't PROVEN you wrong because you were arguing that there exist non-even elements in the set formerly known as the natural numbers, not the set I was referring to as the natural numbers.

As for mathematicians getting upset when something doesn't work out as predicted, you're completely right. The converse, however, is not true. Just because some mathematicians disagree with you (even angrily sometimes) does not mean you are correct. Vehemently arguing that pi is exactly 3 would get responses from mathematicians, and many of them would be calling you a moron - does that mean pi is exactly 3?

>>68
Truth.

>>68
You have serious cognitive difficulties if you don't get what I've already said over and over.

>>70
The only things you've said over and over are "waaah waaah I don't like the accepted definition of the real numbers" and "everyone disagrees with me so I MUST be right."

Until you actually refute something I've said - anything - I'm done posting. Come up with an actual argument if you want to talk with the adults.

>>66
lol, have you ever met a real mathematician?  Homicidal/Suicidal when we are proven wrong?  Ha!  Look at Hilbert's program, which was destroyed by Godel's incompleteness theorem.  Did mathematics die?  No, it didn't - it improved.  I suggest you take you trolling and useless definitions elsewhere.  0.999... = 1 here.

>>38

Then you are claiming that sum(n=1, +inf)[(9)10^-n] is not convergent?

>>73
I'm claiming plain and simple that .9... is not a number, so it makes no sense to compare it to one. It can be represented as a series, as we've already beat the death out of, but ultimately that is irrelevant to the original argument that NotANumber is ANumber. And regarding your comment, you have hopefully been taught the difference between limits and actual values.

>>74
The question is, have you been taught the difference between limits and actual values?  I
m assuming by "actual values", you mean the values of the individual terms of the sequence in question.

The only problem is that the real numbers are by definition equivalence classes of Cauchy sequences.  The identification of such an equivalence class with the actual limit is merely a notational convenience.  ergo 0.999... = 1

>>74
hi whats a number

>>76

A special kind of set.

>>45
0 < .999... < 2.  0, 2 are finite numbers.  Therefore, .999... is also finite.

>>46, 47
EPIC WIN.  ROTFLMAO

>>61
See >>65

>>78
This is the last time I'm going to repeat it: The real numbers are an infinite set of FINITE numbers. Your argument is incorrect.

>>79
fi·nite – adjective
1. having bounds or limits; not infinite; measurable.  [yes]
2. Mathematics. a. (of a set of elements) capable of being completely counted.  [unrelated]
b. not infinite or infinitesimal.  [yes]
c. not zero.  [yes]

Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
(abridged, courtesy of dictionary.com)

My argument is not an assertion about real numbers.  My argument claims that .999... is a finite number.  By the first definition, I placed a definite bound on the number.  It is most definitely not infinite.  I don't care if you believe it's a real number.  The damn thing is finite.