acemuzzy wrote:I'm confused that xkcd have also banned discussion of whether 0.9999.... is 1 or not. That's like not up for debate, Shirley.
The Daddy wrote:Well no, cos you can prove it with algebra. X=0.9(rec) (1) 10x=9.9(r) (2) (2)-(1) 9x=9 x=9/9=1
SpaceGazelle wrote:The experiments don't agree with theory, but that's ok. It doesn't mean the theory is wrong intellectually, it just means the world is complicated.
Lord_Griff wrote:What would a sprinkler do in a vacuum?SpaceGazelle wrote:The experiments don't agree with theory, but that's ok. It doesn't mean the theory is wrong intellectually, it just means the world is complicated.
The Daddy wrote:Well no, cos you can prove it with algebra.
X=0.9(rec) (1)
10x=9.9(r) (2)
(2)-(1)
9x=9
x=9/9=1
acemuzzy wrote:But it's defined as the thing going on forever. So it does go on forever. It's a convergent series. It is 1.
The other way to see it is as a "geometric progression". Each extra decimal place is 1/10th ("r") of the one before. First term 0.9 ("a"). So adding them all up is
Sum = a/(1-r) = (0.9) / (1 - 1/10) = 1.
SpaceGazelle wrote:Lord_Griff wrote:What would a sprinkler do in a vacuum?SpaceGazelle wrote:The experiments don't agree with theory, but that's ok. It doesn't mean the theory is wrong intellectually, it just means the world is complicated.
Same as in air, which is why rockets still work in space.
Lurch666 wrote:The 0.9 rec=1 is also the solution to xenos paradox so if 0.9 rec doesn't=1 then nothing can move. Although with xenos paradox it's 1/2+1/4+1/8+1/16 etc into infinity=1
g.man wrote:I could show you g.man’s funky sprinkler if you like?
GurtTractor wrote:I lack the mathematical intuition to be able to contribute much here, but from what I've read it's basically 'because infinity'.
Silke wrote:a dildo in the ass can only go so far.
The Daddy wrote:Well no, cos you can prove it with algebra.
X=0.9(rec) (1)
10x=9.9(r) (2)
(2)-(1)
9x=9
x=9/9=1
acemuzzy wrote:Unless (drumroll please...) those aren't different values, they're the same value!
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