Bill S.--- Is not the whole point of 'God' that he/she/it is "immortal, invisible" as well as all-seeing and all-knowing? Thus to a believer god just 'is' and for such a believer the existence of god proves the existence of infinity. And before Rev comes roaring along to point out that god transcends personification I shall point to the 'it' in my original definition.

Maybe infinity is proveable in mathematics, I wouldn't know, but god's existence (the state, personification or any other manifestation) cannot be proven. The reason for this is that the existence of god is a matter of personal choice, and is sustained by personal belief. Religion codifies that belief, but is unable to prove the truth of it.

As indeed I am unable to prove that god does not in fact exist.

You are partly right though Bill--- What do we know about god? Only that which other humans have adopted, without actual proof, as their belief, which sometimes is actually quite a lot!