Introduction
Preliminaries on the Collatz Conjecture.
Last updated
Preliminaries on the Collatz Conjecture.
Last updated
Collatz function defined as:
The problem asks whether . We still don't know if this is true (since 1937), but it is conjectured to be so by many. In this work, we will approach the problem in two ways:
Using binary trees to hope for a proof-by-contradiction opportunity
Extending the operation to real numbers and analyzing patterns
It is immediate to observe that showing the conjecture of odd numbers suffices; even numbers eventually reduce to odd numbers via . For this purpose, we have the following two functions:
Reduced Collatz function defined as:
where is the largest number such that result is an odd number.
Reduced Collatz Initializer function defined as:
where is the largest number such that result is an odd number.