talkmagic.co.uk

Arkesus wrote:With the two envelopes problem, it is inferred that nobody knows what you have, .

God knows.

That's because he uses marked envelopes with a cut-out back panel.

Ted wrote:

Lawrence wrote:

Ted wrote:Does the barber shave himself? I can't see a contradiction in that. He's doing it himself so he doesn't have to go to the barber. Is that right?

The problem being that if he is doing it himself then the barber isn't doing it, but he IS the barber...
And if the barber is doing it then he isn't doing it himself

It's a set of all sets that are not members of themselves: i.e. if the barber is in the set then he is not in the set, also if he is not in the set then he is in the set.
As I say, set theory is a load of balls.
I prefer mathematical problems that can be visualised with goats behind doors!

OK, I get what the puzzle is trying to do but I would have thought, in terms of logic, that...

...if he is shaving himself then the barber *is* shaving him, because he is the barber.

There were stipulations that if the men don't shave themselves then the barber does it, but that does not mean that they can't shave themselves and have the barber do it too.

I may not have worded it correctly as I'm trying to recall a set theory lecture from a few years back.
Look up Russell's paradox for what will probably be a better wording (and some stupid maths)

Indeed, the full puzzle has stronger rules.

Wikipedia wrote:Suppose there is a town with just one male barber. In this town, every man keeps himself clean-shaven by doing one of two things:
Shaving himself, or
going to the barber.

Another way to state this is:
The barber shaves all and only those men in town who do not shave themselves.

All this seems perfectly logical, until we pose the paradoxical question:
Who shaves the barber?

This question results in a paradox because, according to the statement above, he can either be shaven by:
himself, or the barber (which happens to be himself).
However, none of these possibilities are valid! This is because:
If the barber does shave himself, then the barber (himself) must not shave himself.
If the barber does not shave himself, then the barber (himself) must shave himself.

Holy hell my brain has seeped out my ears.

Ted wrote:Indeed, the full puzzle has stronger rules.

Apologies. I should have probably just quoted Wiki in the first place.

My hed hurtzzzz...

Mandrake wrote:My hed hurtzzzz...

Blame the Vino.

I usually do.

Not much of a paradox. Either one of the statements in the barber problem is wrong, or the barber has a beard.

It's a bit like saying, "All cows are black and white. A brown cow walks into a field. Wow, what a brain-bending paradox!" It's possible because not all cows are black and white.

Going back to the envelope problem, I think this whole talk of probabilities multiplied by the amount you could win is misplaced. You have a 50% chance of choosing the better envelope. No matter how many times you switch, you still only have a 50% chance of ending up with the higher prize. You can switch or not switch, know how much is in one envelope or not know either sum, it doesn't matter. It's a 50/50 chance.

The Monty Hall maths does work, however, but only because the person running the game always eliminates a losing choice.

That would be to miss the point, since the idea is not to introduce a new set, but to consider the implications of a set of all sets containing sets which are not contained in their selves... Russell, unless I am mistaken, got rid of the paradox by creating a new axiomatic system- but shortly after Godel demonstrated that you can do this as many times as you wish, but there will always be paradoxes; inconsistencies or incompleteness in your axioms.

For example, this statement is not true.

Now, if it is not true, then it is not true that: 'it is not true' and therefore, it must be true- but if it is true, then it is true that: 'it is not true' and therefore it cannot be true. If it is true, then it is true that 'it is not true' and therefore it is not true, because if it was true then it would be false, which means it can't be true.

So there are many problems relating to self containing and self referential sets and indeed it is true that set theory is very silly. However, they are still all very interesting. My favourite is this one, relating to sets containing all sets:

Consider a phonebook which has an infinite number of contacts contained within it and imagine that each phone number was an infinite number of digits long. For the sake of argument, imagine the phone manufacturer wanted each person's number to be unique:
1) 479374658...
2) 564937569...
3) 674956783...
4) 196837583...
.
.
.
(to infinity)

Now, if there truly are an infinite number of such lists of infinite numbers it should seem that every possible list of infinite numbers would be contained somewhere as a telephone number in the phonebook, seeing as there are an infinite number of them. However, there is a mathematical way of creating a new phone number which you know will by definition NOT be contained in these numbers. Take the above list and add one to each consecutive term to obtain a new number:
1) 479374658... 5
2) 564937569... 7
3) 674956783... 5
4) 196837583... 9...
.
.
n)57592...

Now, when you reach another number which corresponds to the number you have constructed with the 'add one' rule, in order to continue with your rule of adding one, whatever number you are up to (in this case two), you still have to add one to: so your new number becomes: 57593, which is different from 57592 which it was previously the same as. Therefore, there is at least one number which certainly doesn't exist in your infinte telephone book... in fact, there are infinitley many which aren't there so therefore, your telephone book can't really be infinite.

Maybe this is another reason not believe in Dopplegangers.

Part-Timer wrote:It's a bit like saying, "All cows are black and white. A brown cow walks into a field. Wow, what a brain-bending paradox!" It's possible because not all cows are black and white.

You can also use set theory to prove that all cows are the same colour

Serioulsy? I feel sorry for the lot of you. And myself for reading through all that. 15 minutes of my life I'll never get back.

PS. Always choose door number 3.