Input resistance | differential amplifier | operational amplifier

See how the value of input resistance drops in an attempt to increase the gain of the operatinal amplifier in differential configuration.

Input resistance | differential amplifier | operational amplifier

[stemscience]

Finate gain of amplifier will cause the potential difference (always). Concept shows approximate analysis (ideal opamp).

[regale]

Isn't the vid = v2-v1. this isn't the potential you measured across op-amp terminal rather it's the potential across the source signals and since there is short circuit how can there be potential difference if we consider your concept.