## The Principle of Green Induction

The Principle of Green Induction is

1) If the first is green

2) If stage n is green then stage n’ is green

Then

All stages are green.

Green can mean a certain condition is true.  In the carry lemma, we proved that the carry out is less than 2 at all places in addition of two numbers using place value with a base of 10.

Green can mean a member of a set.  So a set contains 0 means 0 is green.  If n is green, it is in the set.

So if n is green, then n’ is green is the induction step.  We can also call it the green propagation step in green induction.   We can also call it the green transfer step.

So if 0 is green and green transfers to the next number, then all numbers are green.

If the zero stage is green, and green transfers to the next stage, then all stages are green.

Green transfers to the next stage means that if n is green, this implies n’ is green.

If 0 is green, and green transfers, then all numbers are green.

If 0 is green, and green transfers, then all stages are green.

The Principle of Green Induction is

1) If the first stage is green

2) If green transfers for any stage

Then

All stages are green.

If the first is green and green transfers, then they are all green.