RE: Did you know...?
April 22, 2016 at 4:59 am
(This post was last modified: April 22, 2016 at 5:00 am by Alex K.)
To follow up on rob's example:
if you instead take turns adding and subtracting these numbers in this order,
1/2 - 1/3 + 1/4 - 1/5 + 1/6 - 1/7 ...
you approach a finite number (roughly 0.31).
But the kicker is, you can get *any result you like* out of that very same sum of numbers simply by rearranging it. That's something I found perverse when I first heard it, but it's true.
It's so counter-intuitive because the result only changes if you do an infinite number of swaps, something one cannot easily imagine.
if you instead take turns adding and subtracting these numbers in this order,
1/2 - 1/3 + 1/4 - 1/5 + 1/6 - 1/7 ...
you approach a finite number (roughly 0.31).
But the kicker is, you can get *any result you like* out of that very same sum of numbers simply by rearranging it. That's something I found perverse when I first heard it, but it's true.
It's so counter-intuitive because the result only changes if you do an infinite number of swaps, something one cannot easily imagine.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition