3/5= 3 rounded off to the nearest whole number and then 6=5 which is wrong so rounding is wrong.
Nils Baeté It isn't really a paradox. If x ϵ [2 , 2.5[ then you round x to 2,
if x ϵ [2.5 , 3[ then you round x to 3.
You can divide the real numbers into intervals of equal length (and wich are all half open except for the interval containing 0 wich is an open interval):
... , ]-2.5 , -1.5] , ]-1.5 , -0.5] , ]-0.5 , 0.5[ , [0.5 , 1.5[ ,
[1.5 , 2.5[ , ...
The median values of the intervals (the value wich lies in the middle of each interval) are: ..., -2, -1, 0, 1, 2, ...
The elements of each interval are rounded to the respective median value (so the elements of [1.5 , 2.5[ are rounded to 2 and the elements of [2.5 , 3.5[ are rounded to 3 (like 2.5 wich is rounded to 3)).

You could also divide it like this:
... , [-2.5 , -1.5[ , [-1.5 , -0.5[ , [-0.5 , 0.5] , ]0.5 , 1.5] ,
]1.5 , 2.5] , ...
And in that case you might round 2.5 to 2.

But for the definition of "rounding" they chose the first option. I'm not 100% sure why but maybe it has to do with the fact that R (the collection of the real numbers) itself is an open collection: ]-∞, +∞[
So if you're talking about rounding without any further explaination about it, then you're talking about the first option in wich 2.5 is rounded to 3.

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20 April 2012 1:44 PM

Dark matter does a disappearing act Dark matter has just got even more mysterious. This is the invisible ‘stuff’ which calculations suggest makes up about 83% of the bulk mass of the Universe. Astronomers know it is there even though they cannot see it because by plotting the movement of galaxies and the stars they contain the gravity of the matter we CAN see falls far short. Our galaxy, the Milky Way, for instance, rotates far too rapidly were it to be made only of the visible stars, planets and clouds of dust and gas that we see.  Indeed, most galaxies would fall apart were they not glued together with dark matter, whose existence was first postulated in 1932.