Before we take on a question involving God and infinity, it might be a good idea to warm up with a simple practice problem. Let's start out by designing the ultimate glue. Here are the properties of that glue:
1) It bonds anything to anything else.
2) It forms an unbreakable bond.
3) It sets under even the most adverse conditions.
4) Unfortunately, the lid is stuck to the jar.
You can see the problem. When we try to extend all virtues to their absolute limits, we are likely to discover a problem or two which we didn't expect at first. If we really want to design the ultimate glue, we will need to add a few restrictions:
1) It will not bond the lid to the jar.
2) It will not bond the applicator to the target surface.
By adding these "weaknesses" to our "perfect" glue, we have really made it better. These weaknesses don't need to damage the effectiveness of the glue, they just need to be in place to prevent potential disasters from happening.
Now, returning to our feature question, if God's powers were to be extended to their absolute possible limits, what difficulties might need to be considered? (We are assuming that God does not want to trap himself inside the jar, so to speak.) What kind of limitations might God choose to impose upon himself in order to avoid possible problems? We don't have to be clever to know what limitations God has selected because the Bible tells us specifically. For example:
1) God can't lie (e.g. Titus 1:2)
2) God can't change (e.g. Numbers 23:19)
These two restrictions do not seem to damage the effectiveness of God's power very significantly. In fact, these limitations make Him more to be respected and honored than a fickle and truthless deity would be. But what we are concerned with here is whether God is powerful enough to create a rock that He is not powerful enough to pick up. How might the limitations of consistency and truth help us answer our question?
As is often the case in apparent contradictions, looking at the exact definitions of the terms involved can throw some light on the question. In particular, What is an irresistible force (like God) and what is an immovable object (like a rock which God cannot lift)? These terms have very precise definitions:
1) An irresietible force is a force which no object can resist.
2) An immovable object is an object which no force can move.
By their very definitions, these two items contradict each other. They simply cannot exist at the same time in the same universe. Obviously it is a simple contradiction to create both simultaneously.
Can God contradict himself? If He cannot lie or change His mind, then He cannot. The only way to contradict one's self is to either lie or to change one's mind. Since God cannot do either, He cannot contradict himself. This means He cannot simultaneously produce an immovable object and a force which can move it. This is a natural, logical, and necessary limitation to anything as powerful as God.
It is also a limitation which the Bible has identified for us.