the ideal op-amp
To make op-amp circuits easy to analyze, we first pretend the op-amp is perfect, the way physics class assumes a frictionless pulley. This idealized model strips away the messy real-world limits so you can see the elegant idea underneath, then you add the real limits back later. Three simple assumptions do almost all the work.
The ideal op-amp has: infinite open-loop gain, so any finite output requires essentially zero voltage difference between the inputs; infinite input resistance, so no current at all flows into either input terminal; and zero output resistance, so the output holds its commanded voltage no matter what load you hang on it. We usually also assume infinite bandwidth and zero input offset. Real op-amps are close enough, with gains of 100,000 to over a million, input resistances of megohms to teraohms, and output resistances of tens of ohms, that ideal answers are usually within a fraction of a percent of reality.
These three assumptions, combined with negative feedback, give the two golden rules that make analysis almost trivial. The honest caveat is that ideal is a deliberate simplification, valid only when negative feedback is present and the device is operating within its real limits. Open-loop, or beyond bandwidth, slew rate, or the supply rails, the ideal model fails, and those failures are exactly what the next field studies.
Infinite input resistance means a 1 V source feeding the input through a 1 megohm resistor draws no current, so the source is not loaded at all and the full 1 V reaches the input pin.
Each ideal assumption removes one annoyance, letting the elegant circuit math show through.
Ideal is a simplification, not reality: it holds only with negative feedback and inside the real device's limits. Open-loop, or beyond bandwidth, slew rate, or rails, it breaks down.