# Re: Examples of SQL anomalies?

Date: Tue, 1 Jul 2008 13:29:30 -0700 (PDT)

```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.

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

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

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.

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

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