Quote (Thann @ Apr 24 2010 04:21pm)
As far as I'm concerned, anyone who legitimately believes .999999...=1 is retarded.
I know the logic, and I understand the steps of people's proofs, and the proofs aren't wrong. The logic is..
NONE of these proofs hold water, because all of them are using an infinite decimal.
You guys may as well be trying to say that vertical asymptotes don't exist, because 0=.0000000.....1 therefore approaching the asymptote is the same as being on it...
The only way to describe this "situation" is .9999999 is so close to 1, you MIGHT AS WELL call it 1. It doesn't, and never will = 1.
I'm looking at it, and I see a bunch of 9's in 1 number, and I see a single 1 in the other. Since 9's, in no way shape or form ever =1, they aren't the same.
A baby sees a furry 4 legged animal and is told that "this is a cat". The baby sees a dog, figures, this is furry, has 4 legs, definitely a cat. No, it's a dog.
You can see where the baby is coming from, when they are similar, but they aren't the same. That minor difference (in this analogy blown out of proportion) will ALWAYS make them different.
Like I said, I know where you guys are coming from, and I understand the proofs, but the best way to describe it is "They are so close they MIGHT AS WELL be CALLED the same thing. They are NOT the same thing."
Edit:
I mean honestly, think of it this way:
Does 9=10? NO
Does 99=100? NO
Does 999=1000? NO
Does 9999=10000? NO
What the fuck makes you think the system breaks on an infinity number of 9's, when EVERY SINGLE ONE BEFORE THAT PROVES THAT IT DOESN'T EQUAL.
Edit2:
Tell you what, hit the decimal button (.) then hold your finger on 9 for a long time, and call me when you've managed to get "1" rather than . and a hell of a lot of 9's.
Sources:
-I'm not a retard, and I just thought about it.
So would you agree that the infinite sum of (1/2)^n also does not equal 1 because at no point does any term in the sequence of partial sums equal 1?
This post was edited by darkfire on Apr 24 2010 03:43pm