When I was in a graduate school theology class, someone wondered exactly what "infinity" is. My bachelor's is in math, so I started talking about Georg Cantor's theory of transfinite sets. I gave them Cantor's proof that the cardinality of the irrationals is greater than the cardinality of the rationals.
Some definitions: A set is a collection of things, in this case numbers. The cardinality of a set is the number of things in the set. The rational numbers can be expressed as the ratio of two integers. The irrationals cannot be expressed as such as a ratio, this includes numbers such as pi and e. The cardinality of the rationals -- and the integers as well -- is expressed as Aleph-Null, "aleph" being the first letter of the Hebrew alphabet and "null" is the German word for zero. The cardinality of the irrationals -- and the reals -- is expressed as C.
Cantor showed that if you add or multiply two Aleph-Null sets, you get another Aleph-Null set. That's a restatement of the infinite number of new guests in the hotel with an infinite number of rooms each finding a room. However, if you take Aleph-Null to the Aleph-Null power, you get a set with a larger cardinality, which Cantor called Aleph-1. Similarly, Aleph-1 to the Aleph-1 power is Aleph-2, and so on for an Aleph-Null number of possible Aleph numbers.
A Jesuit (of course) asked me the big question in the subject: Is C equal to Aleph-1? I further mystified the people in the class by saying that this might well be a Goedel question. Kurt Goedel was an Austrian mathematician who showed that in any non-trivial mathematical system, there are questions that you can ask but there is no answer.
The man who asked the question about infinity said that he regretted asking it.
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