I think we should be a little more careful dealing with cardinalities of infinite sets. If A is a proper subset of B and B is infinite, it is not necessarily the case that n(A) < n(B)

Yes I agree too. (actually I said n(A) > n(B) and C is a proper subset of A ). But B is not an infinite set and will never be. So there's not a problem.

Bob

]]>You may well be right but can this be proved satisfactorily ? Here's my analysis of the theory so far:

Here A is the set of all situations that exist, and B is the set of bobbym quotes.

I have created a third set, C = {situations in which bobbym makes a quote}

Clearly n(B) = n(C) and C is a proper subset of A. Thus n(A) > n(B). (Strictly there could be points in B that are not mapped onto but, for this conjecture, we may disregard these *.)

If there is a mapping from points in A to points in B which I'll abbreviate to 'appropriate', and every point in A maps onto a point in B, then the mapping must be many:one.

So some quotes are appropriate for more than one situation, which is why I tried to find a minimum set of quotes that would be appropriate whatever the situation. It's easy to disprove the conjecture if you have a complete list of quotes. I don't.

Bob

* Or redefine B to be the range of the mapping rather than the codomain.

]]>I still feel there is no set of quotes that could possibly cover all situations any more than there is a set of methods or techniques that can solve all problems.

]]>Bob

]]>How are so sure the situation you described exists?

Once again Stefy has shown that I've been talking kabooblydoo. Thank you Stefy and my apologies, Agnishom, for saying that your theory and conjecture is wrong. I have now given this a lot more thought and, whilst I don't yet have a proof one way or the other, I am of the opinion that the conjecture could be true.

Consider these three statements:

That statement is remarkable and almost certainly correct.

That statement is rubbish.

That statement leaves me feeling indifferent about whether it is true or not.

It seems to me that for any situation that exists it is conceivable that one of the above would be an appropriate reaction. I expect as you read this you are hastily trying to think of a situation that cannot have one of the three applied to it. I suggest you save yourself the effort, because it would be easy to add another statement to the list to cover your objection; easier, I think, than making up a counter example. The conjecture doesn't say that a quote can only be applied once. Indeed it is almost implicit that some can be applied more than once, otherwise you would have to have a one-to-one correspondence between situations and quotes and that would be impossible. (I'm ready to prove this, Stefy, if you think you've found another flaw in my arguments.)

So it is possible to conceive of sets of situations and quotes for which the conjecture would hold. But that doesn't prove that bobbym's quotes 'fit the bill.' If you're reading this, bobbym, and I know you read everything on the site, you could easily make those three quotes and make Agnishom happy. I know what a generous and kind hearted person you are, so I look forward to your next post with optimism.

Bob

]]>