Hmm, he lost me on page nine where "complete" is explained.
> Complete means that every sequence of vectors |a1>, |a2>, ... satisfying lim ...
How are the elements of this sequence related? And why are we only interested in the elements where the index n/m goes to infinity? What does that even mean if the sequence is arbitrary?
That's probably why I also can't make sense of this:
> Loosely speaking, saying that a Hilbert space is complete means that it contains all of its limits.
> Complete means that every sequence of vectors |a1>, |a2>, ... satisfying lim ...
How are the elements of this sequence related? And why are we only interested in the elements where the index n/m goes to infinity? What does that even mean if the sequence is arbitrary?
That's probably why I also can't make sense of this:
> Loosely speaking, saying that a Hilbert space is complete means that it contains all of its limits.