The bogosity in Knuth's argument, for any mathematicians who are interested, is that it is - from the point of view of at least one valid way of working with moduli - a patch for something that wasn't broken, and the Wrong Thing. From the point of view of the theory of limits, it's probably the Right Answer, but that doesn't (necessarily) mean that patching the modulus system to work that way is necessary or desirable.
I personally think that Perl's mod, and other computer languages', should
behave the way Knuth's definition suggests, simply because I'd rather my functions gave answers than not. But I admit that it does, in various ways, break the consistency of the definition to do so.
Perl 6 is going to have special features for this kind of 'filled in' definition. Can someone enlarge for this relative newcomer on what use limits
Tiefling (who is imaginary, but appears real at the limit)
-----BEGIN GEEK CODE BLOCK-----
GAT d++ s:- a-- C++ UL P++ L++(+) E? W+(++) N+ o? K w+(--)
!O M- V? PS+ PE- Y PGP- t+ 5 X+ R+++ tv- b+++ DI++++ D+ G+ e++ h!(-) y
------END GEEK CODE BLOCK------
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