A hotel with a countably infinite number of rooms at full occupancy can still accommodate not only 1 more guest or ten more guests or a countably infinite number of new guests, but infinitely many coaches with infinitely many guests each. A veridical paradox that seems absurd on the face of it yet nevertheless is mathematically true. Now my question is whether or not this principle of scaling, transcending infinities carries over to the Divine Infinite Essence? If so then wouldn't the concept of God as Pure Actuality be effectively refuted? We could still say that God is Infinite Actuality but because of this paradoxical aspect of infinity, God would also be infinite potentiality as well. Thus refuting the claim of pure actuality. Also, does this strengthen the case for pantheism/panentheism? If there is anything to this line of thinking then it seems logical that it would indeed strengthen the case for these concepts considerably.Maybe this is a silly question but as a good agnostic I have far more questions than answers and I'm sure most of them are silly. So please, any thoughts, criticisms, rebuttals are welcome and appreciated.