if you want to devide a pizza amongst 2 people then each person gets 1/2
if you want to devide a pizza amongst 3 people then each person gets 1/3
...
if you want to devide a pizza amongst n people then each person gets 1/n
obviously in this case n-->+∞
lim 1/n = 0
n-->+∞
I know that this question probably wasn't intented for me. I just offered a solution.
(01-14-2014, 10:13 PM)BAndrew Wrote: [ -> ]@Bridge
Why is not the following proof valid to you?
We assume that 1 =/= 0,999... =>
(devide by 3) 1/3 =/= 0,333... absurd
Therefore 1=0,999...
How do you explain this?
First of all, I think it is absurd to suggest that you can have an endless series of 3s and yet not 9s. So is 1/3 in fact the exact same as 0.34? Furthermore, you can't use traditional arithmetic with nonreal numbers. You can multiply 0.333 by 3 and get 0.999, but who says that you get the same result with a nonterminating number? Regardless, 0.333 is a crude representation of the simple fraction 1/3. Certainly you aren't suggesting that 1/3 * 3 = 2.999…/3 is a valid answer. It makes unnecessary assumptions. But as I said, I will continue to reject your proofs as using faulty methods to evaluate numbers that it cannot process. There are plenty of examples of faulty systems that produce internally consistent but ultimately facile results, best summed up by the expression "garbage in, garbage out" (GIGO). In my opinion it's a loss of data and approximation - acceptable in most cases - but not robust proof. Clearly you disagree and there is no more discussion to be had.
(01-15-2014, 12:03 AM)Bridge Wrote: [ -> ]First of all, I think it is absurd to suggest that you can have an endless series of 3s and yet not 9s. Furthermore, you can't use traditional arithmetic with nonreal numbers. You can multiply 0.333 by 3 and get 0.999, but who says that you get the same result with a nonterminating number? Regardless, 0.333 is a crude representation of the simple fraction 1/3. Certainly you aren't suggesting that 1/3 * 3 = 2.999…/3 is a valid answer. It makes unnecessary assumptions. But as I said, I will continue to reject your proofs as using faulty methods to evaluate numbers that it cannot process. There are plenty of examples of faulty systems that produce internally consistent but ultimately facile results, best summed up by the expression "garbage in, garbage out" (GIGO). In my opinion it's a loss of data and approximation - acceptable in most cases - but not robust proof. Clearly you disagree and there is no more discussion to be had.
Quote:So is 1/3 in fact the exact same as 0.34?
1/3 is not the same as 0,34, but 0,34=0,3399999999999...
Quote:Furthermore, you can't use traditional arithmetic with nonreal numbers.
What? 0,999... isn't a real number? Are you serious? 0,999... is a perfectly Real number.
Quote:Certainly you aren't suggesting that 1/3 * 3 = 2.999…/3 is a valid answer.
Yes it is. Why not?
Quote:But as I said, I will continue to reject your proofs as using faulty methods to evaluate numbers that it cannot process.
What numbers it cannot process exactly? They are real numbers.
Quote:Math theorems and everything related to it were true before humans where even created. Mathematics existed before humans. Therefore it was not invented by humans, it was discovered by them.
All math teorems are based on previously established methods of math, what is to say that the very basics of math is not an invention? There are no evidence that says that it is in fact natural.
I think math is a language to explain and handle information about stuff around us, natural phenomena. Natural phenomena still exist without math and obey certain rules, yes, but math itself is not a natural phenomena. It's a tool we invented and use to explain natural phenomena, and just like any other tool, math is being expanded upon and in some cases vary, and in rare cases even dysfunction.
I don't believe for a second that math is the truth, that would be making it too easy for myself and in some ways limit my view on the universe and all the wonders it contain.
EDIT: Actually, this is getting very tiring. It's been fun but I'm calling it quits.
The epsilon delta definition of a limit states that lim 1/n as n-->+∞ is as arbitrarily close to zero as n is close to positive infinity. Nowhere did we state that we are actually dividing by infinity, or that division by infinity results in zero. Both are mathematically impossible.
All a limit states is that a number is so arbitrarily close to a value that given any number, the limit is closer to the value than that number.
Oh heavens, the headache on this thread is insane. Reminds me of the talk about Space or Time, or something like that.
This actually explains a lot:
[youtube]7fGoins7q3s[/youtube]
E. Frenkel actually does a great job expaining it.
Also Padilla stated that the "proof" was oversimplified so that a brouder audience could get the idea. Moreover he wrote an article explaining it more mathematically.
source:
http://www.nottingham.ac.uk/~ppzap4/response.html