(adsbygoogle = window.adsbygoogle || []).push({}); Linear Algebra proof

I would appreciate any help with any of the foolowing:

1. Let C be a countable set. Prove that any linear well-ordered on C with the property that whatever c in C there are only finitely elements c` with c`<c, is unduced from the canonical order on N via a bijection N-> C. (N - natural no)

2. Prove that all algebraic numbers (all roots of polynomials with rational coefficients) form a countable subfield of C (complex).

3. Find a representation of the ring C[[x]] as an inverse limit of rings which have finite dimension over C.(complex).

4. Prove that the field Qp is uncountable. (Qp=field of fractions of Zp)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear Algebra proofs

**Physics Forums | Science Articles, Homework Help, Discussion**