About the Collatz Conjecture:
Every body looks at it from "leaves to root" - to use the tree analogy.
I have another approach. My approach is to look at it from the root - the number 1 - and see if, by means of the inverse algorithm functions, I can generate all Counting Numbers.
Here I will wait for a first kind response to this: why is it t that the simple fact that lines 2n and (n-1)/3 - the inverse functions of the algorithm - are obviously continuous and all integers (I mean (n, m) points with m,n integers) belong to one or another isn't enough as a proof?
(note that the generated numbers, by 2n function,: 2,4,6,8,10... plus division generates all naturals: 2,6/2,4,10/2,...)
all integers in those lines are hailstorm numbers. : their big bang like origin - a single point - guarantees that.
So, what I seek is to understand what is to prove!