TITLE: Does the concept of infinity have any practical applications?
QUESTION [10 upvotes]: I know what you're thinking: "of course it has, for example, it can be used to tell you how many times you can go around a circle". But that isn't really true, now is it? You'd be dead or the world would go under long before an infinite amount of loops had been reached.
Are there any practical applications for the concept of infinity? Is it a useful concept in maths at all?
I know that Donald E. Knuth has argued that for all practical purposes, a very, very large number has the same effect as infinity, in his book "Things a Computer Scientist Rarely Talks About" (can't remember the exact quote, nor find it online, unfortunately).
Examples are appreciated.

REPLY [2 votes]: Q: What is the largest prime number ?
A: There is none, because the set of primes is infinite.
Proving an infinite number of primes isn't so difficult, you prove it by contradiction, i.e. by showing that there cannot be a "last prime", the sequence is not finite (the trick is to show that from a given prime deemed the largest one, you can construct another which is... larger). So even though you cannot count  to infinity, you can very well reason about infinity.
Besides ubiquitous appearance in virtually all areas of mathematics, you cannot do without infinity when dealing with continuous phenomena. For instance, you cannot count time, there are too many "instants", and between any two instants there are yet others. By nature, time - and space - cannot be described by finite means (at least as physics currently understands them).
A more abstract usefulness is that working with infinity compells you to find regularity among the studied objects. Working with finite sets in an unstructured/exhaustive way is often possible (for example by means of computers); but infinite collections must somehow be summarized (expressed in comprehension) to become tractable.