Re: Examples of SQL anomalies?

>> What does that mean? <<

The Greeks had a paradox:

1) A cat has one more tail than no cat.
2) No cat has 12 tails.
3) Therefore a cat has 13 tails.

The word "no" is used two different ways. In the (1) "no" is a zero and in (2) it is non-existence.

>> [But there are no members to add!] So what? <<

ab nilo, ex nilo -- from nothing comes nothing.

>> That this is completely a non-problem is most evident with count. Start with a bag containing three bananas. Remove three bananas. How many bananas remain? How is that the least bit hard? <<

But I have to have a bag first and it has to make sense to put bananas in that bag.

>> False! It's not from nothing, and it's not simply a convention. It's the identity of the operator being aggregated. <<

Yes, zero is the additive identity. But this is a convention used to get rid of the empty set problem and preserve easy computations.

>> Again, this [ordered index sets] is not a convention. This form specifies a sequential loop, with a starting number and an ending number. It's inherently sequential. But since we're aggregating a binary function that is both commutative and associative, and since the sequence has no duplicates, the list-theoretic and set-theoretic answers will be identical. <<

I agree that this is pure procedural programming in mathematical disguise; I want a set-oriented solution. This depends on the index set being finite; commutative and associative are a bonus that don't work so well for countably infinite series. You can easily find a set in which you associate the elements in different ways and get different results.

(1 + -1 +1 + -1 +1 ..) = ((1-1) + (1-1) + ..) = 0 (1 + -1 +1 + -1 +1 ..) = (1 + (-1 +1) + (-1 +1) + ..) = 1

The convention is to say it is undefined or that it does not converge. I am a little soft on saying the answer is the set {0, 1}, and defining other such results as the set of naturals or whatever. I have no idea what the rules would be like.

>> You have misapprehended the semantics of the construct. <<

No, I am saying I want to move from "list-theoretic" and "settheoretic"  summations. Received on Tue Jul 01 2008 - 22:29:30 CEST