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Alex,
The answer I provided to Mirko is not really what I had in mind in conceptualizing infinity.
I doubt there is a satisfactory answer to the question, only a redefinition of infinity which makes one more comfortable with the concept and doesn't make the question of how a Big Bang with a finite expansion velocity and finite time frame lead to an infinite Universe, a seemingly impossible one to answer.
In the late 19th century transfinite mathematics was developed which revolutionized the notion of infinity. It was so controversial at the time and opposed by mainstream mathematics, it led to its creator Georg Cantor in having a nervous breakdown and being committed to a mental asylum.
Today the subject is textbook pure mathematics.
A simple example is the real number line which is an infinite set. It extends to -infinity and +infinity.
If you take any interval on the real number line such as [1,2], you find it is also contains an infinite number of real numbers.
The intuitive concept of infinity is blown out of the water, you have two infinite sets, one which contains "fewer" numbers and is a subset of the "larger" infinite set.
If you extend the idea of the number line as forming a 1-dimensional space, you have a smaller infinite space "encapsulated" in a larger infinite space.
Hence the intuitive idea that infinity is larger than anything we can imagine is not terribly useful.
Steven
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