Omnipotence

Can God make a rock so heavy even He cannot lift it?

There are a lot of paradoxes and problems with the idea of an omnipotent god, but this isn't really one of them. It is an interesting question for various reasons; in particular, it is one way of considering the mathematical questions around the concept of infinity. But it's not really as much of a theological question as it sounds.

Consider this question instead. Could God make it so that nine was one more than five? Sure, God could make it so the word we use for the number one more than five was "nine", that's easy, but could he make it so that the concept we currently call "nine" was actually the number that's one more than five? If the answer is no, is that a limit on the "omni" part of "omnipotence"? Could God make it so if you added one to five you got a spicy cheese soup? Could God make colorless green ideas sleep furiously? Could God transform roundness, a property of objects, into a sofa?

When it comes down to it, the rock question is fundamentally the same as these kinds of paradoxes: the paradox is in the question, not the action. No sensible definition of the word "omnipotence" can ever pass that test if you allow questions that are innate contradictions.