Of course God is unfalsifiable

God's existence cannot be proven false.  Since God is unfalsifiable by definition, being unfalsifiable is a property of God's existence.  Since the statement God is unfalsifiable and cannot be disproven is accepted and supported by scientists and Atheists alike, then Occam's Razor shows the simplest explanation to be valid, since a defined and logical statement with scientific and academic consensus is more likely to be true than an argument against it. 

Calculus cannot be proven to be false.  Calculus doesn't wait for some physical evidence to appear and disprove it since Calculus is already logically defined.  We can't prove Calculus exists as a physical thing, but we know Calculus is valid.  Calculus uses self supporting axioms based on the unfalsifiable laws of logic, where abstract theorems do not require physical testability to be valid.  There are many invalid proofs by amateurs who try to disprove Calculus based on a limited understanding of Calculus and a desire to prove Calculus wrong, yet it doesn't matter if you choose not to believe in Calculus or if you declare all of it invalid simply because you don't like it, as such arguments will not make mathematicians everywhere drop the study of Calculus because you don't think it has sound logic.  No matter how you argue, Calculus cannot be falsified. 

Replacing Calculus with God's existence shows the same properties and the same reasons why arguments against them do not work.  Something can be both logically valid and non-falsifiable.

>>19
what do you mean?  I thought Godel's Theorem applied to any recursively defined collection of axioms that allowed us to formalize number theory.  Calculus is usually built up using set theory, which certainly is subject to Godel's Theorem.  Are you talking about axioms for the reals that don't let you talk about integers?
>>20
Only countably many symbols are at our disposal to talk about analysis, and each statement is a finite string of these countably many symbols, hence countably many statements.  In particular, there are only countably many real numbers that can be defined/referred to explicitly in a statement about real numbers; see also "computable number"