Goodwin's theorem (idea)

Apparently an 'unprovable' theorem that the following operations will always produce 0. Start with any natural number - say 7 - and make it into a binary sequence:

7 = 4 + 2 + 1 = 2² + 2¹ + 1 (2⁰)

Then apply the two operations:

• a := Increase powers by one.
• b := Decrease sequence by one.

2² + 2¹ + 1 -(a)-> 2³ + 2² + 2¹ = 13

Then (b) is applied to make 12. This process is continued, (a) then (b), until the number becomes 0.

7, 12,

hmmm..something's gone wrong