User:Leigh.Samphier/Todo

Refactor Definition:Norm/Ring

 * Definition:Norm/Ring


 * Definition:Norm/Division Ring


 * Finite Normed Ring is Field


 * Normed Ring has No Proper Zero Divisors


 * Normed Vector Space Requires Multiplicative Norm on Division Ring

Create theorem Composition of Isometries is Isometry

 * Check Normed Division Ring Completions are Isometric and Isomorphic/Lemma 1

Tidy

 * Quotient of Cauchy Sequences is Metric Completion


 * Quotient Ring of Cauchy Sequences is Normed Division Ring


 * Combination Theorem for Sequences/Normed Division Ring/Inverse Rule

Create second proof to P-adic Norm not Complete on Rational Numbers

 * $\quad \Q_p$ is uncountable, $\Q$ is countable.

Add Definition:Normed Division Algebra to Norm

 * Definition:Normed Division Algebra

Replaced Pages
Leigh.Samphier/Sandbox/Norm Refactor/Normed Division Algebra replaces Definition:Normed Division Algebra

New Pages
Leigh.Samphier/Sandbox/Norm Refactor/Norm/Division Algebra becomes Definition:Norm/Division Algebra

Refactor Definition:Absolute Value

 * Replace Definition:Abstract Absolute Value with Definition:Norm on Division Ring


 * Replace $\struct {\mathbb K, \size{\,\cdot\,}}$ with $\struct {\mathbb K, \norm{\,\cdot\,}}$ in Definition:Valued Field pages.


 * Replace Definition:Abstract Absolute Value, Definition:Absolute Value/Norm Theory and Definition:Absolute Value/Field with appropriate use of Definition:Valued Field