Finger Counting and Peano Axioms

I got the following tweet.

Alexander Bogomolny@CutTheKnotMath

Finger counting to 10 on one hand http://ow.ly/d2tgI

http://www.cut-the-knot.org/ForYoung/FingerCounting.shtml

My tweet back:

Finger Counting is a path to Peano Axioms. Induction can be taught on finite sets.

For finger counting one can also use no fingers held up as the zero state of the hand.  So a fist can be zero.

Finger Induction can start with 0 or 1.

True for first finger step.

Finger hypothesis step.

Finger transfers step.

Finger conclusion step.

So first prove it is true for first finger.  Or use first finger to record some proposition is true.

Assume it is true for some finger.  A variant of this is to assume it is true for last finger of first hand.

Now we do the induction step where we go from the first hand to the second hand.

We assume it is true for the first hand.  (This is also a way to think of course of values induction, whole hand induction we can call it.)

Now we show it jumps to the next hand, the induction step.

Then it continues to travel along fingers.

If we think of an infinite set of hands, we can thing of it as true for infinite sets.

We can also have induction from one student’s hands to the next student’s hands.  This is good for projects or working in pairs or groups.

Name Finger Inductive Examples.

Kentucky Fried Chicken is inductive.

Sticky foods.

Water.

 

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About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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