EDIT: I guess my question is what constitutes mathematical proof. And why does my example not work as an (inductive) mathematical proof? — Benkei
We know dividing by two will always yield either an odd or even number. Once in a while (for larger numbers), we also hit a number that if we divide by 2 we can keep doing that until we reach 1. That series could be infinitely long. So regardless of the number we start with, if we keep going through the two steps of the Collatz sequence we will hit such a number that we can continue to divide by 2 until we reach 1 — Benkei
Even an infinity of sequences hitting your stack, and your stack being infinitely large, doesn't entail that every single number hits the stack right? All it takes is one. — fdrake
You have to be more specific than this to help answer Benk's question "what constitutes mathematical proof?"A mathematical proof for a target statement is a series of statements which logically/deductively show that statement. It can't show something 'like' the target statement, or even make the target statement almost certainly true, it has to show that the target statement is true. The standard is pedantically high. — fdrake
Once in a while (for larger numbers), we also hit a number that if we divide by 2 we can keep doing that until we reach — Benkei
What do you think of the fact that 3n+13n+1 is a straight line and 2m2m is an exponential function? As far as I know, a straight line and an exponential graph intersects at a maximum of only two points. Is this relevanat? :chin: — TheMadFool
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