Sorry, an error occurred while loading the content.

## demons, buckets and balls

Expand Messages
• ... = an infinite number ... = no balls. ... Now I discovered that the trap is Q) At time t 1, how many balls are there in the bucket?. We modify the Q) to
Message 1 of 1 , Dec 1, 2002
I try look for the trap, which is hiding in Phil's "demons, buckets and balls":

>There is a countable infinite number of consecutively numbered balls, a bucket,and two demons.
>Then for n=0,1,...
>At time 1-(2^-(2n)) the first demon places the next 2 balls into the bucket.
>At time 1-(2^-(2n+1)) the second demon removes the lowest numbered ball in the bucket.

>Q) At time t>1, how many balls are there in the bucket?
>A1) The number of balls at time 1-(2^-(2n)) is ever increasing
=> an infinite number
>A2) So the lowest numbered ball still in the bucket is?
=> no balls.
>This calls for wisdom: let him who has understanding reckon the number of the balls...

Now I discovered that the trap is
Q) At time t>1, how many balls are there in the bucket?.
We modify the Q) to be
Q') At time t>1, whether the bucket is empty or not?
Without so much wisdoms , we can check mechanically the formal proof:
Then for n=0,1,...
At time 1-(2^-(2n)) the first demon places the next 2 balls into the bucket.

Namely, we suppose that
the bucket is not empty.

At time 1-(2^-(2n+1)) the second demon removes the lowest numbered ball in the
bucket.

A1) The number of balls at time 1-(2^-(2n)) is ever increasing
=> an infinite number
A2) So the lowest numbered ball still in the bucket is?
=> no balls.

A contradiction, so that we proved
the bucket is empty.

If we had known that the bucket is not empty, namely we had known the pattern of the k-tuple prime, then we ask
Q') At time t>1,how many balls are there in the bucket?
By ever increasing, we proved the number of k-tuple primes is infinite.
There is no any counterexample.

Now I wish,understanding my proof of twin prime conjecture
http://www.primepuzzles.net/conjectures/twinconjliusproof.doc
will be more easy.

China.
Liu Fengsui.
Your message has been successfully submitted and would be delivered to recipients shortly.