Bijections Cardinality head segments and so on

When we define addition by cardinality we require a lot of machinery to be already in place.

We want to add 2 + 3 = 5.

We need to have 2,3, 5 as numbers.

We need initial counting segments or counting head segments from 1 to 2, 1 to 3 and 1 to 5.

We need to be able to find sets without common elements in bijection with the counting head segments 2 and 3.

We need to be able to do a bijection with the counting head segment 5.

When we do the addition identities, we have to do even more.

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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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