EDB — 057

[057]Prerequisites:[02D]↺↻,[053]↺↻,[055]↺↻.Difficulty:**.

Let \(V\) be a real vector space. Let \(A,B\) be two Hamel bases (see [02D]↺↻). Show that \(|A|=|B|\). (This result is known as ”Dimension theorem”)

More in general, let \(L,G⊆ V\), if the vectors in \(L\) are linearly independent, and \(G\) generates \(V\), show that \(|L|≤ |G|\).