Exploring Quantum Physics - Mystery about the resolution of the identity solved!

I was confused with the resolution of the identity, it states that if $| \psi_i \rangle$ is a basis, then

$\sum\limits_{i=0}^{\infty}{|\psi\rangle\langle\psi_i|} = 1$.

After reading Quantum mechanics demystified, finally understood the meaning of the above.

As $\psi$ is an abstract vector, we should NOT think of it as a wavefunction, or a tuple, or whatever, instead, we define $|a\rangle\langle b|$ as an operator to mean $|a\rangle\langle b|( |c\rangle) = |a\rangle(\langle b|c\rangle)$,

Now it suddenly become clear! The 1 in the above identity is not the real/complex number 1, but the identity operator that takes a vector to itself!