What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.
The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful.
Does there exist an Infinity outside ourselves? Is that infinity One, immanent and permanent, necessarily having substance, since He is infinite and if He lacked matter He would be limited, necessarily possessing intelligence since He is infinite and, lacking intelligence, He would be in that sense finite. Does this Infinity inspire in us the idea of essense, while to ourselves we can only attribute the idea of existence? In order words, is He not the whole of which we are but the part?
The Universe is very, very big.It also loves a paradox. For example, it has some extremely strict rules.Rule number one: Nothing lasts forever.Not you or your family or your house or your planet or the sun. It is an absolute rule. Therefore when someone says that their love will never die, it means that their love is not real, for everything that is real dies. Rule number two: Everything lasts forever.