Op Amp Q: Will Vout Go to Zero When Inverting Input is Greater?

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Garengineer
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Hello. I have a very quick op amp question. I'm trying to understand an omp amp. My question is will vout of an op amp go to zero if the inverting input is greater than the non inverting input ( even if there's a negative/positive feedback)?
 
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Opamps normally have a positive and a negative supply.

If the inverting input is greater than the non inverting input then the output will go towards the negative supply voltage, but usually it can't be exactly the same as the negative supply.
There is always a volt or two difference between the output and the negative supply.

Similarly, the output cannot be the same as the positive supply either.