Answer by Michael Hardy for Confusion about the Hamel Basis
I take this to mean that $S$ is a Hamel basis if $S$ is linearly independent, and there is no linearly independent set $T$ for which $|T|>|S|$. That is a flaw in your "Hamel basis definition 1".That...
View ArticleAnswer by Eric Wofsey for Confusion about the Hamel Basis
Your definitions of "linearly independent", "basis", and "orthonormal basis" are all correct. In particular, an orthonormal basis for an infinite-dimensional Hilbert space is not actually a basis...
View ArticleConfusion about the Hamel Basis
Alright, so I'm reading a book on Hilbert spaces and functional analysis, and here it defines a "Hamel basis" to be a "maximal linearly independent set". I take this to mean that $S$ is a Hamel basis...
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