Goodstein Sequence
Given a Hereditary Representation of a number 
in Base, let 
be theNonnegative Integer which results if we syntactically replace each 
by 
(i.e., 
is a basechange operator that `bumps the base' from up to ). The Hereditary Representation of 266 in base 2 is
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so bumping the base from 2 to 3 yields
Now repeatedly bump the base and subtract 1,
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etc. Starting this procedure at an Integer
gives the Goodstein sequence 
. Amazingly,despite the apparent rapid increase in the terms of the sequence, Goodstein's Theorem states that
is 0 for any and any sufficiently large 
.See also Goodstein's Theorem, Hereditary Representation- Cardioid
- Cardioid Caustic
- Cardioid Evolute
- Cardioid Inverse Curve
- Cardioid Involute
- Cardioid Pedal Curve
- Cards
- Carleman's Inequality
- Carlson-Levin Constant
- Carlson's Theorem
- Carlyle Circle
- Carmichael Condition
- Carmichael Function
- Carmichael Number
- Carmichael's Conjecture
- Carmichael Sequence
- Carmichael's Theorem
- Carmichael's Totient Function Conjecture
- Carnot's Polygon Theorem
- Carnot's Theorem
- Carotid-Kundalini Fractal
- Carotid-Kundalini Function
- Carry
- Carrying Capacity
- Cartan Matrix