Counting by bins Peano Axioms for bins

We think of the whole numbers, 0,1,2, etc. as being primary and existing as the bedrock we build math of.  However, another view is that we count bins and the bins can contain objects.   We can be counting whole numbers of bins and the same Peano Axiom rules apply to those binds.

  1. Zero a tick.
  2. A tick then a tick.
  3. Zero no mom.
  4. Not zero, one mom.
  5. Zero green, green transfers, all green.
  1. Zero a node.
  2. A node then a node.
  3. Zero node no mom node.
  4. Not zero node, one mom node.
  5. Zero node green, green transfers along nodes, all nodes green.


  1. Zero a bin.
  2. A bin then a bin.
  3. Zero no mom bin.
  4. Not zero bin, one mom bin.
  5. Zero bin green, green transfers along bins, all bins green.

Whole numbers can be thought of as labels of bins or of nodes or actually being bins.

We can have bins of 2, bins of 3 etc.

This is how we transition to fractions.  See the next post.



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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