# Re: Examples of SQL anomalies?

From: JOG <jog_at_cs.nott.ac.uk>
Date: Tue, 1 Jul 2008 14:37:57 -0700 (PDT)

On Jul 1, 9:29 pm, -CELKO- <jcelko..._at_earthlink.net> wrote:
> >> What does that mean? <<
>
> 1) A cat has one more tail than no cat.

Asking how many tails a "no cat" has is like asking how many tails the colour blue has. The answer is not zero, the answer is "category error" - the question makes no sense. As a consequence there is no paradox here, because the first line is in error.

Anyhow, there is no such thing as a non-existent cat - a thing has to exist (whether abstractly or physically) for it to be a "thing" in the first place, by definition. Regards, J.

> 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 "set-
> theoretic" summations.
Received on Tue Jul 01 2008 - 23:37:57 CEST

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