Of course a 1000 years is nothing from "nature's perspective". But for mankind it is a loooong time. And future generations will have to deal with the nuclear damage/waste.
It is just not right that future generations have to deal with contaminated areas and nuclear waste just so that I can run my 3 airconditioners 24/7. (I do not, but I know many who do...)
There is a huge difference between "nuclear" damage and damage down to the environment through e.g. hydropower: Any damage we do to the environment with hydro/solar/wind power will be gone quickly as nature can fix itself over time.
With nuclear damage nature cannot fix itself quickly. It takes a 1000 years or so.
That is why I think that it is not responsible to use nuclear energy because if we mess up our children's children have to deal with our mistakes. I am not saying that there will be a (another) huge nuclear accident, but nobody can deny that there could be one.
Sorry, but out of that one typo (and he must mention that x begins with a '1') I do not think anything is wrong in that "original" proof.
I even think that it can be made far more general than yours, it really implies that any two (real!!) numbers x,y where:
x/y = 1/4 (Not only x=1,y=4!!)
have the property that
X'/Y' = 1/4,where
X' = 10x+6 and Y' = 10y+24
This is far more general and the original 166/664 thingy just falls out as a special case:
(with, if you really want, a trivial induction)
x=1, y=4 and noting what you noted;-) (x(n+1)=..)
One could proof that note, but that would be reeeal overkill.
Jan
P.S. One could generalize the proof a lot further though, but that would really just be for the fun of it.
Slashdot Mirror
Doesn't reading some threads remind you of a certain scene from Life of Brian? ;-)
First thing I thought of reading the editorial
It is just not right that future generations have to deal with contaminated areas and nuclear waste just so that I can run my 3 airconditioners 24/7. (I do not, but I know many who do...)
That is why I think that it is not responsible to use nuclear energy because if we mess up our children's children have to deal with our mistakes. I am not saying that there will be a (another) huge nuclear accident, but nobody can deny that there could be one.
We must not take that chance!
Sorry, but out of that one typo (and he must mention that x begins with a '1') I do not think anything is wrong in that "original" proof.
I even think that it can be made far more general than yours, it really implies that any two (real!!) numbers x,y where:
x/y = 1/4 (Not only x=1,y=4!!)
have the property that
X'/Y' = 1/4 ,where
X' = 10x+6 and Y' = 10y+24
This is far more general and the original 166/664 thingy just falls out as a special case: (with, if you really want, a trivial induction) x=1, y=4 and noting what you noted ;-) (x(n+1)=..)
One could proof that note, but that would be reeeal overkill.
Jan
P.S. One could generalize the proof a lot further though, but that would really just be for the fun of it.