... written¹

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

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... ket.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 number).

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