26 Mar
2012
26 Mar
'12
10:31 a.m.
Jerzy Karczmarczuk
Le 26/03/2012 02:41, Chris Smith a écrit :
Of course there are rings for which it's possible to represent the elements as lists. Nevertheless, there is definitely not one that defines (+) = zipWith (+), as did the one I was responding to.
What?
The additive structure does not define a ring. The multiplication can be a Legion, all different.
I'm not sure I understand what you're saying there. If you were asking about why there is no ring on [a] that defines (+) = zipWith (+), then here's why. By that definition, you have [1,2,3] + [4,5] = [5,7]. But also [1,2,42] + [4,5] = [5,7]. Addition by [4,5] is not one-to-one, so [4,5] cannot be invertible. -- Chris Smith