That is a good question! I don’t know of a way of defining a q-analog of a complex number per se, usually q-analogs are used for integer quantities! Sometimes the q in the series can stand for a complex number, but that’s a different use than I believe you’re imagining. Thanks for asking!

]]>Can we define q analog of a complex number? ]]>

I think the point is that it’s either true or it’s false. So just one example of it being false with be sufficient evidence. To disprove the theory.

]]>Infinity doesn’t solve for everything though and The Collatz conjecture has two outcomes:

1) They all reduce to one

2) There is a magical (large!) number that actually drops into a loop where it gets bigger before dropping back to itself.

Infinity allows (if anything) for more ‘chance’ of a single magic number out there and the maximum steps do grow as you search for bigger numbers.

less than 10 is 9, which has 19 steps,

less than 100 is 97, which has 118 steps,

less than 1000 is 871, which has 178 steps,

less than 104 is 6171, which has 261 steps,

less than 105 is 77031, which has 350 steps,

Even though there are an infinite number of values for x there are also an infinite number of moves possible to get back to 1 if it doesn’t connect with pre-existing lines which do lead back to 1. Maybe working out the chances of it meeting or not meeting a pre-existing line is the way to go. From previous experiments that chance seems infinitely small.

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