Input impedance of inverting amplifier clarification
When we talk about the input resistance of a circuit, we're describing how it affect the other circuit that is providing the input signal. 

Specifically, we want to know, in order to change the input current by i amps, how much do we need to change the input voltage? That's why the input resistance is, by definition, \$ \dfrac{\mathrm{d}v_i}{\mathrm{d}i_i}\$. 

So what's the input resistance of this circuit?

The key point is that in this configuration, as long as we avoid saturating the op-amp output, the inverting input of the op-amp is a virtual ground. The feedback in the circuit operates to keep that node at 0 V. So whatever input current we want, by Ohm's Law, the required input voltage is \$\mathrm{R_{in}}\times{}i_{i}\$. Therefore the input resistance is Rin.


  Then there are answers like this that mention that input impedance is infinity. 


That answer was talking about the input resistance of the op-amp, which was assumed to be ideal, not the input resistance of the whole circuit.