Abstract: This proposal aims to approach the Turing Halting Problem by introducing the concepts of non-computable functions and an additional state, "pinfHalt," which denotes a program that halts only after infinite time. By redefining the problem through these concepts, I argue that the classica...

If we show that all numbers up to a certain number n, reach to a value less than themselves in their respective Collatz orbit, and then based on this further show that n+1 also reaches to a value less than itself in its sequence, then is this a valid proof for Collatz conjecture, provided proof o...