Dr. Carrier, you stated that "all numbers exist" in an infinite quantity, and that something "that has no location exists nowhere and what exists nowhere does not exist". Where exactly do numbers exist (in infinite quantity no less)?

Everywhere.

Numbers are words that refer to quantities. Anywhere all quantities exist, all numbers exist. Any region of space-time contains all quantities (that region can be infinitely divided and paired one-to-one with every natural number, for example). Therefore anywhere where there is a region of space-time, all numbers exist. If naturalism is true, then there is at least one region of space-time. Therefore, if naturalism is true, then all numbers exist.

Conversely, to claim all numbers don't exist entails God does not know all numbers and is therefore not omniscient. Because if he knows a number, it exists, being located in his mind (assuming his mind exists somewhere, since if God exists nowhere, then indeed God doesn't exist). Therefore, anyone who claims God knows all numbers must also accept the existence of an actual infinity. Therefore the impossibility of an actual infinity can never be a true premise for them.

I discuss the ontology of numbers (and provide links for further study) in the following link (both in the main entry and in the following discussion comments).

Defining Naturalism