For an ideal opamp the unity gain buffer has a voltage gain of exactly 1; so Vin = Vout:
But if we neglect all non-idealities except the DC open loop gain Aol, how can we mathematically/analytically demonstrate the effect of the Aol to the error between the input and the output voltage? I have read once that if Aol=infinity then Vin = Vout but if Aol=10000 then Vin is not exactly equal to Vout. But I cannot derive myself why neither I can find a source in internet for derivation of this.