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proof invalidNo
(6/2)*3+1=10
(2/2)*3+1=4 , (4/2)*3+1=7 so they cannot converge into one value as it has passed 6 as an odd number
your argument incorrectly assumes that if one number eventually reaches another under the Collatz rules, then the second number must also be able to reach the first, when in reality, the Collatz function is not reversible. every number has a unique next value, but a number may have multiple, one, or no predecessors. For example, 6 goes to 3, then to 10, to 5, to 16, to 8, then to 4, yet 4 to 2 to 1 to 4 never returns to 6. this is not a contradiction, because the Collatz conjecture only requires that every sequence eventually reaches 1, not that paths can be traced backwards. therefore, it is invalid because it treats the Collatz map as if it were reversible when it is not.