Axioms

Let every number be arbitrarily composed of two numbers.

Let the number table exist as suchâ€¦

0=(0,1)

1=(1,1)

2=(2,2)

3=(3,3)

4=(4,4)â€¦and so on

Let no "ordered pair" be represented by another "further" ordered pair.

Let the first number of the number chosen be labeled as z1

Let the second number of the number chosen be labeled as z2

Let multiplication exist as followsâ€¦

(A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA )

Let division exist as followsâ€¦

(A/B) = ( z1forA/z2forB )

(B/A) = ( z1forB/z2forA )

Let every number be arbitrarily composed of two numbers.

Let the number table exist as suchâ€¦

0=(0,1)

1=(1,1)

2=(2,2)

3=(3,3)

4=(4,4)â€¦and so on

Let no "ordered pair" be represented by another "further" ordered pair.

Let the first number of the number chosen be labeled as z1

Let the second number of the number chosen be labeled as z2

Let multiplication exist as followsâ€¦

(A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA )

Let division exist as followsâ€¦

(A/B) = ( z1forA/z2forB )

(B/A) = ( z1forB/z2forA )

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