In what sense is God infinite?
A distinction is made between "potential infinity" and "actual infinity". Potential infinity being the infinity we talk about when we say something is unlimited, or extends without bounds. Actual infinity refers to the size of a set or collection of things, and it is this notion of infinity that Cantor conceptualized with his infinite cardinals. When we say that God is infinite, I would argue we mean it as a potential infinity, not as an actual infinity. That is to say, God is infinite in that His goodness, mercy, love, what-have-you is unbounded, without limit, or without end. Actual infinity answers the question "how many?". When applied to God, the answer is 1. If you were to ask the question "what is the size of the collection of concepts that are contained in God's intellect" on the other hand, this would be more amenable to the type of analysis given above. However, in that case, I think the question is incoherent. It is akin to asking