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More than 80 years has passed since the Collatz conjecture has been proposed, but since then there has been no concrete proof as to why it is stuck in the 4 to 2 to 1 loop endlessly. There had been various attempts to find the reason as to why this infinite loop occurs, but there hasn’t been any widely recognized proof for the Collatz conjecture.

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This paper details a different approach to explain why this infinite loop occurs and at the same time explain why the Collatz conjecture is similar to a computer source code. Section 2, 3, 4, and 5 details the process used to determine the purpose of 2n and n+1 functions inside an iterative loop, while section 6 and 7 reveals the logical reasoning behind how the 2n+2 algebraic expression was obtained based on 3n+1 or 2n+n+1.

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Section 8 provides proof for 2n+2 as the hidden algebraic expression of the Collatz conjecture, while both sections 9 and 10 provides proof that it is also possible to get stuck in the -4 to -2 to -1 loop endlessly when n is any negative odd integer by simply replacing addition with subtraction. Sections 11 provides the key reason why the Collatz conjecture is getting stuck in an endless loop of 4 to 2 to 1.

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