15/05/16 08:55:20.67 3tqJtzYJ.net
>>397 補足
" This is equivalent to the condition that every x ∈ V can be written in precisely one way as
∑cixi （i∈F）
where F is finite, ci ∈ K and xi ∈ B for each i ∈ F."
この表記はイタリア流？ （i∈F）where F is finite は、日本では見かけない
下記と対比してください。Fが１から始まる自然数の有限集合ってことかな？
URLﾘﾝｸ(mathworld.wolfram.com)
Hamel Basis
A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {Uα} such that every real number β has a unique representation of the form
β=∑ ri*Uαi,(i=1～n)
where ri is rational and n depends on β.
The axiom of choice is equivalent to the statement: "Every vector space has a vector space basis," and this is the only justification for the existence of a Hamel basis.