User:Leigh.Samphier/Todo

Replace $\mathcal C \paren {R}$ with $\mathcal C$ in theorems

 * $\quad$Definition:Ring of Cauchy Sequences
 * $\quad$Convergent Sequences to Zero are Maximal Ideal
 * $\quad$Quotient Ring of Cauchy Sequences is Division Ring
 * $\quad$Embedding Normed Division Ring into Ring of Cauchy Sequences
 * $\quad$Embedding Division Ring into Quotient Ring of Cauchy Sequences
 * $\quad$Quotient Ring of Cauchy Sequences is Normed Division Ring

Add converse proof for Maximal Ideal iff Quotient Ring is Field

 * $\quad$Using converse proof from Maximal Left and Right Ideal iff Quotient Ring is Division Ring

Sort out Maximal Ideal iff Quotient Ring is Division Ring

 * Replace links to Maximal Ideal iff Quotient Ring is Division Ring with links to Maximal Left and Right Ideal iff Quotient Ring is Division Ring
 * Propose Maximal Ideal iff Quotient Ring is Division Ring for deletion

Extend Embedding Division Ring into Quotient Ring of Cauchy Sequences

 * $\quad$Extend to include Definition:Distance-Preserving Mapping

Create Definition:Normed Division Ring Completion
Completion: Distance-Preserving Monomorphism $\phi:R_1 \to R_2: R_2$ is a metric completion of $\phi \paren {R_1}$

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

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