Is Tripling Odd Numbers Necessary in the Collatz Conjecture?

[fizzzzzzzzzzzy]

Hey, i was reading about the Collatz conjecture, where, if you take a integer, divide it by 2 if its even and triple it then add one if it's odd, and do it over and over again, the result would be one. I was thinking, "wouldnt it have the same effect if you didnt triple odd numbers?" am i wrong?

 

[matt grime]

"the same effect"? What do you mean? What you've just described is clearly different, and obviously converges to 1 (after any two operations, you must have decreased the number you started with, hence it must converge).

 

[tacman]

Yes, you are correct. The Collatz conjecture states that starting with any positive integer and repeatedly applying the described process will eventually lead to the number 1. However, if you were to only divide by 2 when the number is even and not triple odd numbers, you would still eventually reach 1. This is because dividing by 2 and then tripling the result is the same as just multiplying by 1.5, so the end result would still be 1. However, the conjecture specifically states the process of dividing by 2 and tripling odd numbers to make it simpler and more interesting.