Tag Archives: Skolem

Every odd positive integer is connected to 1

The elements at the ‘horizon’ of the diagram are the irrational elements >1 in the extension field Q[sqrt5] encoded in binary in the Stern-Brocot tree. In that tree between every two integer values to the right of 1 there is a subtree isomorphic to the whole left side (the subtree between 0 and 1). As encodedContinue reading “Every odd positive integer is connected to 1”

Collatz Proof

Consider the positive integers in base 2, in binary notation. Define prefix: the digits left of the first pair (from the right) of identical digits along with the left digit of that pair. Define tail: the digits to the right of the prefix. Define the Collatz function: Consider the positive integers in binary in countingContinue reading “Collatz Proof”