A Proof Related to the Collatz Conjecture

[pwithee24]

Above is a visual proof that for all odd numbers n>1, n eventually leads to a number m such that m immediately leads to a number p such that p<m. Any questions, comments, or suggestions are appreciated!

 

[Cubist]

I added some row and column labels to help facilitate discussion. I find your grid and written explanation very confusing. I almost didn't reply because I literally have no idea what is going on

For example, where are the values for n & m shown on your grid (if they are shown at all)? Where does the "7" in cell D2 come from? (It doesn't appear to be generated by either of the equations in A2 or B2).

Regarding the arrows...
- I think that if the number at the arrow's base is x, then the arrow points at a value in the row above that is f(x)
- if the above is true, then why isn't there an arrow from cell D3 to H2?

 

[JeffM]

It seems to me that you are trying to show a pattern by a finite number of examples. That is not a proof.