>>14056045x = 1*1*1*1*1*... (we assume that 1^infinity is defined to be this)
count the 1's and index them like so:
1_1 * 1_2 * 1_3 * ...
Now, take the product of all the even indexed 1's and multiply it by the product of the odd indexed 1's
x = 1_1 * 1_3 * 1_5 * ... * 1_2 * 1_4 * 1_6 ...
call the product of the odd indexed 1's P and the product of even index 1's Q
There are the same number of odds and evens alone as there are natural numbers, so every index of P and Q can just be mapped to the naturals, so P and Q are equal to x
x = x*x
so x is either 1 or 0
