Counting on Definition of Addition

We define counting on by one and give it the special prime symbol.



We define addition by two rules for counting on.

Counting on by zero rule

n+0 = n

Counting on by one more rule

m+n’ = (m+n)’

This says that counting on by one more of the right addend equals counting on by one more from the previous sum.


2+0 = 2

Suppose we have already done

2+3 = 5.

Now we want to do 2+4.  Here 4 = 3′ we also know.

2+4 = 2+3′ = (2+3)’ = 5′ = 6

This is how we use that 2+3 = 5 in the substitution step.


If the rules are too difficult just call them facts.

Counting on Facts


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.
This entry was posted in Addition as counting, Addition Definitions, Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Counting on Definition of Addition. Bookmark the permalink.

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