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After all, what is more difficult to conceive of: an infinite number of infinities or an Almighty? When I first discovered this fact about the infinity of infinities during Set Theory class my senior year in college, I was completely mesmerized. ?śHow could this be???I mused. Infinity means just that?”infinity. No end in sight; something that goes on forever. So how could there be more than one? Even millions. Billions? An infinity of them? Yet strange realities such as these are what we derive from mathematics. Once these realities become validated, our faith in mathematics and in a higher being becomes more real. Faith is evidence or proof of those things we cannot see. Faith validates that even though we cannot see something, i.e. God, that that something is still real.
We see and experience applications of mathematics in the real world everyday. We have automobiles and electricity and television and the computer, the latter of which has harnessed the understanding and power of binary arithmetic. We can see these applications, touch these applications and enjoy these applications. They are real. Yet the very foundations on which such applications are built, the axiomatic systems on which all applications ultimately derive from theorems provable based on those axioms, are, according to Kurt Gödel?™s work, based on a certain degree of faith. The leap from proof to truth, in the end, is always based on faith.
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