Category Archives: Counting on Rules of Arithmetic

Why use Counting on Identities instead of Cardinality rule for addition

Define prime by 1=0′, 2 = 1′,  3 = 2′, 4=3′, etc. The counting on identities are 2+0 = 2 2+3′ = (2+3)’ Here we call 2 the anchor or base and 3 the shift.  The latter is not standard, … Continue reading

Posted in Cardinality, Cardinality Definition of Addition, Counting on Definition of Addition, Counting on Rules of Arithmetic, Counting on v Cardinality | 1 Comment

Counting on induction

We need to decide on terminology and meaning for mathematical induction for counting on. If you start from 0 and count on to any number and then count on to the next number, then you count on to every number. … Continue reading

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Counting on Facts and addition

If rules are too difficult just call them facts.   We define counting on by one and give it the special prime symbol. Counting on Facts 1=0′ 2=1′ We define addition by two facts for counting on. Counting on by … Continue reading

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Counting on Definition of Addition

We define counting on by one and give it the special prime symbol. 1=0′ 2=1′ 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’ = … Continue reading

Posted in Addition as counting, Addition Definitions, Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Counting on Definition of Addition | Leave a comment

Counting on Rules of Arithmetic CORA

Counting on Rules of Arithmetic. We count on from a starting number like 3 by a second number, the count on number or shift number like 2. 3+2 means start at 3 and count on by 2. We imagine we … Continue reading

Posted in Counting on Definition of Addition, Counting on Rules of Arithmetic, Kindergarten Counting On, Peano Axioms for Number Line | 3 Comments