Re: Examples of SQL anomalies?

On Jul 1, 9:29 pm, -CELKO- <jcelko...@xxxxxxxxxxxxx> wrote:
What does that mean? <<

The Greeks had a paradox:
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.

.

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