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I am a retired US Navy Data Systems Technician where I receive some of the finest digital training on the planet. This training was taught at the transistor level, logic gate by logic gate of mainframe computers. This imparted an engineers understanding of each computer under study, and a masters understanding of binary logic.

During my career, I spent 3 years teaching a US Navy combat system maintenance course in the late 1980’s. (The best tour of my career.) As part of the course, I conveyed an intense knowledge of the binary processes to my students. And, as anyone who has taught knows, you never truly understand a subject until you have taught it several times. This course include binary floating point math. Floating Point is the foundational math used by all computers through current microprocessors and is the foundation of this proof.

The need to know the intricacies of floating point math has long since past. Processors are pretty much on disposable cards and chips. So, except for those in computer chip design or extreme engineering challenges where understanding some of the shortcomings in accuracy of todays computers still matter, this depth of knowledge is no longer needed. The need to know exactly how binary worked within the processor so one can diagnose a broken computer to the transistor level when 1+1=3 is not necessary for break/fix. Diagnose to the card and toss it.

I was introduced to Collatz Conjecture just a few short years ago, an immediately recognized this as a binary centric process. That was the easy part. I have been through multiple iterations of this proof to try to fully explain the two processes which can be found in each Collatz iteration. In each review of this paper, something new presents its self or the wording can be improved.

Please feel free to email thoughts, counter considerations or would just like to talk Collatz or Fermat. terry@mathpossibilites.com

I believe existence is like a language, as where you don't have to know every word in a language to understand, so it is with not having to know everything about existence in order to understand it.

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