But your argument is somewhat circular; a number (or any symbol critical to the definition of math) is an arbitrary symbol of a thought, or a description of something that you can comprehend. Arbitrary and logic don't get along.
God, like numbers, either exists or does not. Period. No amount of arguing or "proofs" will change that. It doesn't matter how intelligent we are, or how much sense the argument makes. God is either a one or a zero.