Godel's incompleteness theorum

Maybe the barber has extremely low testosterone and can't grow a beard or he uses Nair???or being a man maybe he just sets his beard on fire? If he uses Nair then he technically is not shaving! Lol

Do these guys have to send their blades out for honing?

This is not a paradox. This is an example of ill-defined sets.

James.

I would also like to see an example of a mathematical theory being contradictory

How about this one.
3 guys want to rent a boat. They each have 10 dollars a piece. So the get to the boat rental and ask the guy how much is it to rent a boat. He responds that it's 30 dollars to rent a boat. Well that's cool, they each have 10 bucks a piece x 3 guys = 30 dollars. So they give the guy the money and he goes into the boss. He tells the boss that here's 30 dollars for a boat rental. The boss says hey, there's a special today it's only 25 dollars to rent a boat today so here is 5 bucks give them back their change. So the guy is trying to figure how he is going to split 5 dollars between 3 guys so he decides to keep 2 dollars as a tip and gives each guy a dollar back. So each guy gets a dollar back so they really paid 9 dollars each. 9 dollars x 3 guys = 27 dollars plus the 2 bucks the kid kept = 29 dollars!! What happened to the other dollar????

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Originally Posted by Tsunami

How about this one. 3 guys want to rent a boat. They each have 10 dollars a piece. So the get to the boat rental and ask the guy how much is it to rent a boat. He responds that it's 30 dollars to rent a boat. Well that's cool, they each have 10 bucks a piece x 3 guys = 30 dollars. So they give the guy the money and he goes into the boss. He tells the boss that here's 30 dollars for a boat rental. The boss says hey, there's a special today it's only 25 dollars to rent a boat today so here is 5 bucks give them back their change. So the guy is trying to figure how he is going to split 5 dollars between 3 guys so he decides to keep 2 dollars as a tip and gives each guy a dollar back. So each guy gets a dollar back so they really paid 9 dollars each. 9 dollars x 3 guys = 27 dollars plus the 2 bucks the kid kept = 29 dollars!! What happened to the other dollar????

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There's not an extra dollar. You were supposed to subtract the 2 bucks the kid kept to equal the 25 dollars it cost to rent the boat. Adding 2 bucks just adds an unnecessary and irrelevant element to the story!

True but you can not solve the problem with multiplication. Only with addition or subtraction

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Originally Posted by Jimbo

This is not a paradox. This is an example of ill-defined sets.

James.

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It certainly (in my understanding) does not have to do with Godel's incompleteness theorem.

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Originally Posted by TwistedOak

I would also like to see an example of a mathematical theory being contradictory

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If this is related to Godel's incompleteness theory, it doesn't talk about contradictions.
Instead, it says (proves) that within each non-trivial axiomatic system, there will be propositions which cannot be proven or disproven either way. In other words, the axiomatic system is incomplete. And indeed, in mathematics, there are propositions which can be identified as unprovable. The math is beyond me, but there are classes of problems that within a certain context, can be proven to be unprovable either way.

My head hurts.