(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)

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# Linear Algebra proofs

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