GOODSTEIN SEQUENCE
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G(2)
HEREDITARY BASE-2
2 = 2¹
SEQUENCE STEPS
G(2): base 2: 2 = 2¹ → replace 2→3: 3¹ = 3, subtract 1 → 2
base 3: 2 → replace 3→4: 2, subtract 1 → 1
base 4: 1 → subtract 1 → 0
The simplest case. Starting from 2, the sequence reaches 0 in just 3 steps.
→ 0
Reaches 0 at step 3. A gentle introduction — the real monsters start at 4.
Even though every Goodstein sequence reaches 0, Peano arithmetic cannot prove this fact.
Goodstein (1944) · unprovable in PA · rotates daily