... written^1.1

Actually, this is strictly true only for finite-dimensional spaces. Only a special subset of denumerably infinite dimensional spaces have this property ( i.e., they are complete). However, because a ket space must be complete if it is to represent the states of a microscopic system, we can restrict our attention to this special subset.

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... ket.^1.2

We can now appreciate the elegance of Dirac's notation. The combination of a bra and a ket yields a ``bra(c)ket'' (which is just a complex number).

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