Negative feedback using op amps?
You are confusing 'inverting' with 'negative feedback'.

Open loop







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Figure 1: op-amp with open-loop inverting mode.

In Figure 1 the op-amp will amplify the difference between its inputs by the open loop gain. Let's say the open loop gain is 1,000,000 and we apply +1 mV at the '-' input. Since it is higher than the '+' input the output will go to -1 mV x 1000000 = -1000 V. (Obviously on a real op-amp it will stop at the negative supply rail.)

This circuit would not make a good amplifier as the gain would not be controllable, any variation or drift in the input offsets would wreak havoc with the output and any non-linearities of the amplifier would go un-checked. It might, however, make a useable comparitor to detect if the input voltage was above or below, in this case, zero volts.

Negative feedback


  Negative feedback occurs when some function of the output of a system,
  process, or mechanism is fed back in a manner that tends to reduce the
  fluctuations in the output, whether caused by changes in the input or
  by other disturbances. 
  Wikipedia.


Applying negative feedback brings the output under control.







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Figure 2: inverting op-amp with negative feedback. Figure 3: non-inverting opamp with positive feedback.

Now if we apply negative feedback by putting back R2 the output counters the input. Imagine the operation as a sequence:


Vin = 0. Vout = 0.
Vin = 1 V. Vout = 0 at this instant. R1 and R2 form a voltage divider and the '-' input is at 0.5 V.
Vout starts to swing negative. This pulls the '-' input back towards 0 V.
The output settles down at Vout = -1 V.


In this configuration the output will move to whatever voltage makes the '-' input the same as the '+' input. This will occur when \$Vout = -Vin \frac {R2}{R1}\$.

Positive feedback

Figure 3 shows the amplifier with positive feedback.

In this situation the scenario will be as follows:


Vin = 0. Vout = 0.
Vin = 1mV. Vout still at 0 so '+' input goes to +0.5 mV.
Vout starts to rise. The '+' input voltage starts to follow it at about half the rate (because of the voltage divider effect).
Vout hits the + supply rail.


This circuit is often used to make a Schmitt trigger to add some hysteresis so that turn-on and turn-off points are different.

Non-inverting with negative feedback







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Figure 4. Non-inverting amplifier.

The non-inverting amplifier also uses negative feedback although in a different fashion. I find it most useful to think that the op-amp is 'happy' or stable when both inputs are at the some potential. In this case it's when \$Vout = Vin \frac {R1 + R2}{R1} = Vin (1 + \frac {R2}{R1}) \$.