Proof of 1 Not equal 0.999...

0*infinity=(0+0+0+0...)=0 (x+0=x x=0)
1=0.999... (agreed) 1-0.999...=0
(type 1) 1-0.999...=(1/10)*(1/10)*(1/10)... (from division by 10, 1-0.9 etc)
ab=0 if a or b=0; 1/10=0 ;10*1/10=10*0 ;1=0 ;x*1=x*0 ;x=0
(type 2) (1/10)*(1/10)*(1/10) ...=(1/10)^infinity=1/infinity=0
1/infinity=0 then 0*infinity=1 bu 0*infinity=0 ;1=0 ;x*1=x*0; x=0
Every number equals zero .(by 1=0.999...)

I'm not >>40

>>37
if we take .999... to mean a decimal point followed by an "infinite" amount (perhaps it's better to say, uncountable amount) of nines afterwards then the answer to the question:
"what number is between .999... and 1?" is none. Or rather there exists no distinct number between .999... and 1 because they are the same number. Just like there are no numbers between 0 and .000... because they become the same number.

>>38
that number would actually be less than both 1 and .999... since both .999...0 and .999... have the "same" amount of digits (infinitly so for both). If one was subtract the former from the latter, one would get .000...9 which is greater than than the subtraction of 1.000...0 and .999...9 which yields .000... and therefore .999...0 is farther from one than .999... is. You would somehow have to create a number that has more digits than infinity in order to create a number between 1 and .999...

>>41
"(perhaps it's better to say, uncountable amount)"
No, it's not better, because uncountable means something different.

>>41
>If one was subtract the former from the latter, one would get .000...9

.000...9 is not a number. That expression makes no fucking sense. You can't write something *after* an infinite number of digits, there is no after, THERE IS NO END.

If one was to subtract the former from the latter, one would get ZERO, ZIP, NADA, SAGE THIS FUCKING THREAD DIE DIE DIE

In my very first class, on my very first day in university, the professor had everyone in the entire lecture hall chant in unison, "Infinity is not a number."

Best thing he ever taught us.


Also, I just noticed the Wikipedia page "Proof that 0.999... equals 1" has been merged into the 0.999... page. That's kindof boring. In any case, what with FrozenVoid liking Wikipedia so much, how has no one linked this yet?

http://en.wikipedia.org/wiki/0.999...
>In mathematics, the recurring decimal 0.999… , which is also written as 0.\bar{9} , 0.\dot{9} or \ 0.(9), denotes a real number. Notably, this number is equal to 1. In other words, "0.999…" represents the same number as the symbol "1".

>>42
>No, it's not better, because uncountable means something different.

Would 0.999... with aleph_null 9s be a different number than 0.999... with aleph_one 9s?

>>47
.999... with aleph-one 9s doesn't really make sense. Aleph-zero is the cardinality of N; it seems obvious that the number of digits in .999... is of similar size.

>>1
Please die.

>>49

In a fire.

>>47
Would 0.999... with aleph_null 9s be a different number than 0.999... with aleph_one 9s?

As >>48 said, there aren't aleph_one 9s. They're countable, look:

0.9 9 9 9 9 9 9 ...
---1 2 3 4 5 6 7 ...

There isn't a different number with aleph_one 9s or a way of writing it with aleph_one 9s; the decimal expansion is by definition just a sequence of numbers, hence any decimal expansion has countably many digits.

Let x=.99999..
Then 10x=9.999..
So 10x-x=(9.999..)-(.999..)
Then 9x=9
Thus, x=1.

GG.

1/1 = 1.

1/.999... = 1.000...
10/9.999... = 1.000...

Therefore, 1 = .999...

There is no .000...0001 at the end of .999... because the nines go on infinitely.

you assume at the top that .999 = 1 its the only way your formula will work

>>52
thread over.

If x is equal to .9999 as in step one then it is .9999

>>56
Yes, and 0.999... = 1.

Chart .999... on a chart and youll never get to point 1. End.

>>58
How do you chart a single number? Because that's what 0.999... is. It isn't a fucking sequence you useless shithead.

.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 to infinity will eventually (lol) reach the number 1.

didn't read any of the previous posts.

>>62
Really? Ok, graph the sequence 3.01 please.

It's the same sequence as .999... (decimal expansion), but with a0 = 3, a2 = 1, and all other a's as zero. The limit of that sequence is 3.01000..., which is what you're looking for.

http://en.wikipedia.org/wiki/Decimal_expansion
First formula there.

Dealing with trolls kills braincells.

Save your braincells, and just move on.

>>64
Tell me, do the sequences {1/2, 3/4, 7/8, 15/16, ... } and {2/3, 8/9, 26/27, ... } approach the same value? If so, why do you think that the sequences {0.9, 0.99, 0.999, ... } and {1.0, 1.00, 1.000, ...} do not? The article you linked specifically states that a number is equal to an infinite sum of the form Sum[i=0,+inf](a_i/10^i). And, ironically, it specifically links the article about proving 0.999... = 1!

>>67
I don't. I know that. I have no idea why you thought I didn't.

>>68
>>69
K, so I reply to >>64 and get two responses from obviously different people. Please try to determine which of you morons I'm addressing before rushing to hit the reply button next time.

>>64
>>68
>>71
Same person.

>>70
Only >>69 is guilty of failing to understand whom >>67 was talking to, as well as of ultimate fail in the ways of math.

>>71
Rereading >>64 I can see you weren't really disagreeing with me, sorry. Nevertheless, you mostly missed my point. Although you can take the sequence of successive one-digit approximations to a number and graph it as a sequence of course, I was objecting to people saying "graph 0.999... and see that it approaches 1 but never equals it", primarily because this kind of statement is just a fancy way of hiding behind the "omg numbers are like, processes, dude!" that so many deniers use. Also because it's silly to say "graph a number as a sequence" when there are infinitely many sequences which converge to any number.

>>73
Sorry, you must be confused. In math, you have to actually have an argument, not just say "lol no way dude". GTFO.

>>75
Again, argument? You don't get to just declare yourself correct.

>>77
Present an argument or GTFO.

>>79
Ah good, thanks for clearing that up. Now I'll just use my psychic powers to figure out which argument is yours.