Leigh.Samphier/Sandbox

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RED

Continuing Svetlana Book

**Coherent Sequence is Partial Sum of P-adic Expansion

Leigh.Samphier/Sandbox/Partial Sums of P-adic Expansion forms Coherent Sequence

**Leigh.Samphier/Sandbox/Definition:P-adic Numbers as Quotient of Cauchy Sequences

Leigh.Samphier/Sandbox/P-adic Expansion is a Cauchy Sequence in P-adic Norm/Represents a P-adic Number

Leigh.Samphier/Sandbox/Integers Arbitrarily Close to Rationals in Valuation Ring of P-adic Norm

Leigh.Samphier/Sandbox/Equivalence Class in P-adic Integers Contains Unique Coherent Sequence

Leigh.Samphier/Sandbox/Equivalence Class in P-adic Integers Contains Unique Coherent Sequence/P-adic Expansion

Leigh.Samphier/Sandbox/Equivalence Class in P-adic Integers Contains Unique P-adic Expansion

Leigh.Samphier/Sandbox/Equivalence Class in P-adic Numbers Contains Unique P-adic Expansion

Every P-adic Number is Limit of P-adic Expansion

Leigh.Samphier/Sandbox/P-adic Norm is Index of First Nonzero Coefficient in P-adic Expansion

Leigh.Samphier/Sandbox/Definition:P-adic Units

Leigh.Samphier/Sandbox/Set of P-adic Units is Unit Sphere

Leigh.Samphier/Sandbox/Characterization of Rational P-adic Units

Leigh.Samphier/Sandbox/P-adic Expansion of P-adic Units

Matroids

Loops and Parallel Elements

To be completed.

Properties of Independent Sets and Bases

Leigh.Samphier/Sandbox/Independent Set can be Augmented by Larger Independent Set

Leigh.Samphier/Sandbox/All Bases of Matroid have same Cardinality

Leigh.Samphier/Sandbox/Matroid satisfies Base Axiom

Leigh.Samphier/Sandbox/Alternative Axiomatization of Matroid