Quote (khoi @ Jun 10 2010 05:53am)

one stupid question for mankind and one giant leap for trolls.

Quote (kegman909650 @ May 20 2010 11:08pm)

I have the answer right here:

Sum of an infinite geometric series.

a/(1-r) where a = the first number of the series and r = the common ratio

0.9999 repeating can be seen as a geometric series like so: 9/10 + 9/100 + 9/1000 + 9/10000 ... etc

a/(1-r) turns into (9/10)/(1-1/10), or 9/9.

One of the simplest mathematical proofs is that anything divided by itself equals 1, so 9/9 = 1, and if 0.9 repeating equals 9/9, then it also equals 1.

Quote (ass666 @ 15 Jun 2010 17:51)

0.9999999999999999999999999 is like saying
∑(9/10^n,n,1,k)
so take the limit of k ∞ and you get 1
therefore 0.999999999.... = 1

http://img408.imageshack.us/img408/6194/msp428419b3e84ghc5791ge.gif

an equivalent equation would be

lim_(k->infinity) (10^k-1)/10^k

Simplify (10^k-1)/10^k assuming k>0 [which it is, starts at 1 ∞] giving 1-1/10^k:

= lim_(k->infinity) (1-1/10^k)

The limit of a difference is the difference of the limits:

= 1-lim_(k->infinity) 1/10^k

The limit of a quotient is the quotient of the limits:

= 1-1/(lim_(k->infinity) 10^k)

Using the continuity of 10^k at k = infinity write lim_(k->infinity) 10^k as 10^(lim_(k->infinity) k):

= 1-1/10^(lim_(k->infinity) k)

The limit of k as k approaches infinity is infinity:

= 1

Quote (Snakesrcool @ Jun 10 2010 11:26am)

I've made one of these.

LET X = Y = 1

x^2 - x^2 = 0
x^2 - y^2 = 0                (Substitute Y in for X)
(x+y)(x-y) = 0              (Difference of squares)
(x+y) = 0                      (Divide by (x-y))
x = -y
1 = -1

If you'll notice, proofs like the one I just put here, and the one you saw that states 1=2, have some internal error in them. In this proof I divided by 0 (x-y).

EDIT: There have been many proofs already posted on this thread about how .9999... = 1 so I won't add more of them, but if you don't believe that .99999... = 1:
http://mathforum.org/library/drmath/view/57035.html
Dr. Ethan has a doctorate in mathematics, his word has weight to it.

EDIT 2:



Is 0.00....1 a number? No.

Quote (Hammer_Hdin @ Jun 18 2010 06:31am)

(a+b)(a-b)
= a^2 - b^2
= 1^2 - 1^2
=1 - 1
=0

Please explain to me how you came to the conclusion that x = -y