Re: My talk about Godel to the post-grads.

David C. Ullrich wrote:
On Thu, 17 Jul 2008 19:46:35 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Wed, 16 Jul 2008 13:18:10 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

I just think you are stupid Ulrich.

I think you are stupid because you think (if you have thought about it at all) that a term can play a role (in a union) even though it plays no role. Let's simplify that:

You think that letters are signs.

You won't be able to understand that, I know. So I will give you an example. Remember the definition of a union? Well, consider the case that x is only in A.
This makes no sense. Do you mean that x is an element of A and
B is empty, or that x is an element of A and B can contain things
other than x or what?
Why mention B? Unless you can give a reason why you must consider B, then there's no reason why you must consider it. In fact, advocating the employment of terms with no significance is a non-starter, whether these terms are empty, full, hidden, non-existent, or jump on to stage accompanied by tumultous applause.

And you think _I'm_ stupid (as well as every other mathematician
on the planet, evidently).

You didn't seem to read what I wrote.

First, you ignored my _questions_ regarding what you
meant by your "consider the case where x is only in A".

Second, you've been saying that there's something incorrect about the definition. If it _were_ true that B was irrelevant, that wouldn't make anything about the definition incorrect, it would just mean the definition was somewhat silly.

And third, your idea that B is irrelevant is simply wrong.

Suppose that A = {1,2,3} and x = 1.

If B = {4} then x is only in A but AuB = {1,2,3,4}.
If B = {5} then x is only in A but AuB = {1,2,3,5}.

So B is not irrelevant.

Of course that may not be an example of the situation
you had in mind - it's hard to know because what you
wrote was so poorly phrased and you refuse to clarify.
Perhaps you meant "consider the case where B is
empty". Yes, if B is empty then AuB = A. Here
we've _specified_ what B is - you're saying that
the definition is wrong because in a certian case
where we know what B is we don't need to know
the value of B. Makes just as much sense as
complaining that b is irrelevant in a + b because
if b = 0 then a + b = a.
David C. Ullrich

"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)

So you don't know why you bring B into AuB except that it just seems to polish off the picture you have always been taught. I have an Aunty you know. She has three legs. But only two have grown.
.

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