Is Infinity truly the limit? God and the concept of infinity

When it comes to concepts such as "infinity," the simple understanding is that "infinity" is "infinity" and nothing can be greater than "infinity." That is the idea behind classical theism's idea of the infinity of God, where God is beyond and greater than finitude. Creaturely existence is finite, while the only uncreated One is infinite. Likewise, since "infinity" is "infinite," therefore one cannot speak of "infinite parts," for parts by definition are finite (c.f. James E. Dolezal, All that is in God, 48).

The problem for classical theism in this area is that it is based upon flawed metaphysics. In this particular case on the issue of "infinity," it is based upon a flawed mathematical theory. The 19th century German mathematician Georg Cantor figured out that infinity is not what we have traditionally thought it to be. Rather, "infinities" are actually transfinites, and one infinity can be larger than another infinity. This can be seen as the cardinality of the set of all real numbers (R) is larger than the cardinality of the set of all natural numbers (N), but both sets are sets of infinite numbers, as can be shown below:

To sum up, using one-to-one correspondence, it can be shown that the set of all real numbers is larger than the set of all natural numbers, since there exists a real number that cannot be mapped to the set of natural numbers. To phrase it another word, the cardinality of all real numbers (c, = א1?) is larger than the cardinality of all natural numbers (א0). Thus, one infinity is larger than another infinity. And even larger than these infinities is the power set of all natural numbers (P{c}), and so on and so forth.

Once we realize the strange world of infinities, we will realize that classical theism's view of "infinity" is not tenable. We can and must hold that God is infinite, but we cannot ever claim that the "infinity" of God is anything that can be argued from the "infinity(ies)" below. In other words, most theologizing about infinity that depends on natural theology or mathematics or science is in error. The infinity from below is of the creation and not the Creator, and it is unscientific to think otherwise.

This is one reason why I do not respect the new defenders of classical theism: in this time and age after all that we have learned of science and math, they ignorantly turned their backs on modern theories by ignoring them, thinking that by going back to the "Golden Age" of Scholasticism they will make [Reformed] Christianity great again! Roman Catholicism tried that at Vatican I and the Anti-Modernist Oath, and it didn't turn out too well, did it?